Finite Math Examples

$5 x + 7 y + 7 z = - 17$ , $- 4 x + y - 3 Z = - 12$

Step 1

Solve the equation for $x$ .

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Move all terms not containing $x$ to the right side of the equation.

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Subtract $7 y$ from both sides of the equation.

$5 x + 7 z = - 17 - 7 y$

$- 4 x + y - 3 Z = - 12$

Subtract $7 z$ from both sides of the equation.

$5 x = - 17 - 7 y - 7 z$

$- 4 x + y - 3 Z = - 12$

$5 x = - 17 - 7 y - 7 z$

$- 4 x + y - 3 Z = - 12$

Divide each term in $5 x = - 17 - 7 y - 7 z$ by $5$ and simplify.

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Divide each term in $5 x = - 17 - 7 y - 7 z$ by $5$ .

$\frac{5 x}{5} = \frac{- 17}{5} + \frac{- 7 y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 x}{5} = \frac{- 17}{5} + \frac{- 7 y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

Divide $x$ by $1$ .

$x = \frac{- 17}{5} + \frac{- 7 y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

$x = \frac{- 17}{5} + \frac{- 7 y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

$x = \frac{- 17}{5} + \frac{- 7 y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

Simplify the right side.

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Simplify each term.

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Move the negative in front of the fraction.

$x = - \frac{17}{5} + \frac{- 7 y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

Move the negative in front of the fraction.

$x = - \frac{17}{5} - \frac{(7) y}{5} + \frac{- 7 z}{5}$

$- 4 x + y - 3 Z = - 12$

Move the negative in front of the fraction.

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 4 x + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 4 x + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 4 x + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 4 x + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 4 x + y - 3 Z = - 12$

Step 2

Solve the equation for $y$ .

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Simplify $- 4 (- \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}) + y - 3 Z$ .

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Simplify each term.

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Apply the distributive property.

$- 4 (- \frac{17}{5}) - 4 (- \frac{7 y}{5}) - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify.

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Multiply $- 4 (- \frac{17}{5})$ .

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Multiply $- 1$ by $- 4$ .

$4 (\frac{17}{5}) - 4 (- \frac{7 y}{5}) - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine $4$ and $\frac{17}{5}$ .

$\frac{4 \cdot 17}{5} - 4 (- \frac{7 y}{5}) - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $4$ by $17$ .

$\frac{68}{5} - 4 (- \frac{7 y}{5}) - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$\frac{68}{5} - 4 (- \frac{7 y}{5}) - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $- 4 (- \frac{7 y}{5})$ .

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Multiply $- 1$ by $- 4$ .

$\frac{68}{5} + 4 (\frac{7 y}{5}) - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine $4$ and $\frac{7 y}{5}$ .

$\frac{68}{5} + \frac{4 (7 y)}{5} - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $7$ by $4$ .

$\frac{68}{5} + \frac{28 y}{5} - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$\frac{68}{5} + \frac{28 y}{5} - 4 (- \frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $- 4 (- \frac{7 z}{5})$ .

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Multiply $- 1$ by $- 4$ .

$\frac{68}{5} + \frac{28 y}{5} + 4 (\frac{7 z}{5}) + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine $4$ and $\frac{7 z}{5}$ .

$\frac{68}{5} + \frac{28 y}{5} + \frac{4 (7 z)}{5} + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $7$ by $4$ .

$\frac{68}{5} + \frac{28 y}{5} + \frac{28 z}{5} + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$\frac{68}{5} + \frac{28 y}{5} + \frac{28 z}{5} + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$\frac{68}{5} + \frac{28 y}{5} + \frac{28 z}{5} + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$\frac{68}{5} + \frac{28 y}{5} + \frac{28 z}{5} + y - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

To write $y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{68}{5} + \frac{28 z}{5} + \frac{28 y}{5} + y \cdot \frac{5}{5} - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify terms.

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Combine $y$ and $\frac{5}{5}$ .

$\frac{68}{5} + \frac{28 z}{5} + \frac{28 y}{5} + \frac{y \cdot 5}{5} - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine the numerators over the common denominator.

$\frac{68}{5} + \frac{28 z}{5} + \frac{28 y + y \cdot 5}{5} - 3 Z = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine the numerators over the common denominator.

$- 3 Z + \frac{68 + 28 z + 28 y + y \cdot 5}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 3 Z + \frac{68 + 28 z + 28 y + y \cdot 5}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Move $5$ to the left of $y$ .

$- 3 Z + \frac{68 + 28 z + 28 y + 5 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Add $28 y$ and $5 y$ .

$- 3 Z + \frac{68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

To write $- 3 Z$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 3 Z \cdot \frac{5}{5} + \frac{68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine $- 3 Z$ and $\frac{5}{5}$ .

$\frac{- 3 Z \cdot 5}{5} + \frac{68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Combine the numerators over the common denominator.

$\frac{- 3 Z \cdot 5 + 68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $5$ by $- 3$ .

$\frac{- 15 Z + 68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $- 1$ out of $- 15 Z$ .

$\frac{- (15 Z) + 68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Rewrite $68$ as $- 1 (- 68)$ .

$\frac{- (15 Z) - 1 \cdot - 68 + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $- 1$ out of $- (15 Z) - 1 (- 68)$ .

$\frac{- (15 Z - 68) + 28 z + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $- 1$ out of $28 z$ .

$\frac{- (15 Z - 68) - (- 28 z) + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $- 1$ out of $- (15 Z - 68) - (- 28 z)$ .

$\frac{- (15 Z - 68 - 28 z) + 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $- 1$ out of $33 y$ .

$\frac{- (15 Z - 68 - 28 z) - (- 33 y)}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $- 1$ out of $- (15 Z - 68 - 28 z) - (- 33 y)$ .

$\frac{- (15 Z - 68 - 28 z - 33 y)}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify the expression.

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Rewrite $- (15 Z - 68 - 28 z - 33 y)$ as $- 1 (15 Z - 68 - 28 z - 33 y)$ .

$\frac{- 1 (15 Z - 68 - 28 z - 33 y)}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Move the negative in front of the fraction.

$- \frac{15 Z - 68 - 28 z - 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- \frac{15 Z - 68 - 28 z - 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- \frac{15 Z - 68 - 28 z - 33 y}{5} = - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{15 Z - 68 - 28 z - 33 y}{5}) = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify both sides of the equation.

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Simplify the left side.

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Simplify $- 5 (- \frac{15 Z - 68 - 28 z - 33 y}{5})$ .

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{15 Z - 68 - 28 z - 33 y}{5}$ into the numerator.

$- 5 \frac{- (15 Z - 68 - 28 z - 33 y)}{5} = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Factor $5$ out of $- 5$ .

$5 (- 1) (\frac{- (15 Z - 68 - 28 z - 33 y)}{5}) = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Cancel the common factor.

$5 \cdot (- 1 \frac{- (15 Z - 68 - 28 z - 33 y)}{5}) = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Rewrite the expression.

$15 Z - 68 - 28 z - 33 y = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$15 Z - 68 - 28 z - 33 y = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 (15 Z - 68 - 28 z - 33 y) = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Multiply $15 Z - 68 - 28 z - 33 y$ by $1$ .

$15 Z - 68 - 28 z - 33 y = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$15 Z - 68 - 28 z - 33 y = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$15 Z - 68 - 28 z - 33 y = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$15 Z - 68 - 28 z - 33 y = - 5 \cdot - 12$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify the right side.

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Multiply $- 5$ by $- 12$ .

$15 Z - 68 - 28 z - 33 y = 60$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$15 Z - 68 - 28 z - 33 y = 60$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$15 Z - 68 - 28 z - 33 y = 60$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Move all terms not containing $y$ to the right side of the equation.

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Subtract $15 Z$ from both sides of the equation.

$- 68 - 28 z - 33 y = 60 - 15 Z$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Add $68$ to both sides of the equation.

$- 28 z - 33 y = 60 - 15 Z + 68$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Add $28 z$ to both sides of the equation.

$- 33 y = 60 - 15 Z + 68 + 28 z$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Add $60$ and $68$ .

$- 33 y = - 15 Z + 128 + 28 z$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$- 33 y = - 15 Z + 128 + 28 z$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Divide each term in $- 33 y = - 15 Z + 128 + 28 z$ by $- 33$ and simplify.

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Divide each term in $- 33 y = - 15 Z + 128 + 28 z$ by $- 33$ .

$\frac{- 33 y}{- 33} = \frac{- 15 Z}{- 33} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify the left side.

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Cancel the common factor of $- 33$ .

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Cancel the common factor.

$\frac{- 33 y}{- 33} = \frac{- 15 Z}{- 33} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Divide $y$ by $1$ .

$y = \frac{- 15 Z}{- 33} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{- 15 Z}{- 33} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{- 15 Z}{- 33} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Simplify the right side.

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Simplify each term.

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Cancel the common factor of $- 15$ and $- 33$ .

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Factor $- 3$ out of $- 15 Z$ .

$y = \frac{- 3 (5 Z)}{- 33} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Cancel the common factors.

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Factor $- 3$ out of $- 33$ .

$y = \frac{- 3 (5 Z)}{- 3 \cdot 11} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Cancel the common factor.

$y = \frac{- 3 (5 Z)}{- 3 \cdot 11} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Rewrite the expression.

$y = \frac{5 Z}{11} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{5 Z}{11} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{5 Z}{11} + \frac{128}{- 33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Move the negative in front of the fraction.

$y = \frac{5 Z}{11} - \frac{128}{33} + \frac{28 z}{- 33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Move the negative in front of the fraction.

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$x = - \frac{17}{5} - \frac{7 y}{5} - \frac{7 z}{5}$

Step 3

Solve the equation for $z$ .

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Simplify $5 (- \frac{17}{5} - \frac{7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33})}{5} - \frac{7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z$ .

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Simplify each term.

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Combine the numerators over the common denominator.

$5 (\frac{- 17 - 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify each term.

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Apply the distributive property.

$5 (\frac{- 17 - 7 \frac{5 Z}{11} - 7 (- \frac{128}{33}) - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify.

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Multiply $- 7 \frac{5 Z}{11}$ .

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Combine $- 7$ and $\frac{5 Z}{11}$ .

$5 (\frac{- 17 + \frac{- 7 (5 Z)}{11} - 7 (- \frac{128}{33}) - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $5$ by $- 7$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} - 7 (- \frac{128}{33}) - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- 17 + \frac{- 35 Z}{11} - 7 (- \frac{128}{33}) - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $- 7 (- \frac{128}{33})$ .

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Multiply $- 1$ by $- 7$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} + 7 (\frac{128}{33}) - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine $7$ and $\frac{128}{33}$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{7 \cdot 128}{33} - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $7$ by $128$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} - 7 (- \frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $- 7 (- \frac{28 z}{33})$ .

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Multiply $- 1$ by $- 7$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} + 7 (\frac{28 z}{33}) - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine $7$ and $\frac{28 z}{33}$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} + \frac{7 (28 z)}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $28$ by $7$ .

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- 17 + \frac{- 35 Z}{11} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Move the negative in front of the fraction.

$5 (\frac{- 17 - \frac{35 Z}{11} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- 17 - \frac{35 Z}{11} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

To write $- 17$ as a fraction with a common denominator, multiply by $\frac{33}{33}$ .

$5 (\frac{- \frac{35 Z}{11} - 17 \cdot \frac{33}{33} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine $- 17$ and $\frac{33}{33}$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{- 17 \cdot 33}{33} + \frac{896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the numerators over the common denominator.

$5 (\frac{- \frac{35 Z}{11} + \frac{- 17 \cdot 33 + 896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify the numerator.

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Multiply $- 17$ by $33$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{- 561 + 896}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Add $- 561$ and $896$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{335}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- \frac{35 Z}{11} + \frac{335}{33} + \frac{196 z}{33} - 7 z}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

To write $- 7 z$ as a fraction with a common denominator, multiply by $\frac{33}{33}$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{335}{33} + \frac{196 z}{33} - 7 z \cdot \frac{33}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine $- 7 z$ and $\frac{33}{33}$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{335}{33} + \frac{196 z}{33} + \frac{- 7 z \cdot 33}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the numerators over the common denominator.

$5 (\frac{- \frac{35 Z}{11} + \frac{335}{33} + \frac{196 z - 7 z \cdot 33}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the numerators over the common denominator.

$5 (\frac{\frac{- 35 Z}{11} + \frac{335 + 196 z - 7 z \cdot 33}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $33$ by $- 7$ .

$5 (\frac{\frac{- 35 Z}{11} + \frac{335 + 196 z - 231 z}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Subtract $231 z$ from $196 z$ .

$5 (\frac{\frac{- 35 Z}{11} + \frac{335 - 35 z}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify each term.

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Move the negative in front of the fraction.

$5 (\frac{- \frac{(35) Z}{11} + \frac{335 - 35 z}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $5$ out of $335 - 35 z$ .

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Factor $5$ out of $335$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{5 (67) - 35 z}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $5$ out of $- 35 z$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{5 (67) + 5 (- 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $5$ out of $5 (67) + 5 (- 7 z)$ .

$5 (\frac{- \frac{35 Z}{11} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- \frac{35 Z}{11} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- \frac{35 Z}{11} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

To write $- \frac{35 Z}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 (\frac{- \frac{35 Z}{11} \cdot \frac{3}{3} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Write each expression with a common denominator of $33$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{35 Z}{11}$ by $\frac{3}{3}$ .

$5 (\frac{- \frac{35 Z \cdot 3}{11 \cdot 3} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $11$ by $3$ .

$5 (\frac{- \frac{35 Z \cdot 3}{33} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{- \frac{35 Z \cdot 3}{33} + \frac{5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the numerators over the common denominator.

$5 (\frac{\frac{- 35 Z \cdot 3 + 5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify the numerator.

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Factor $5$ out of $- 35 Z \cdot 3 + 5 (67 - 7 z)$ .

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Factor $5$ out of $- 35 Z \cdot 3$ .

$5 (\frac{\frac{5 (- 7 Z \cdot 3) + 5 (67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $5$ out of $5 (- 7 Z \cdot 3) + 5 (67 - 7 z)$ .

$5 (\frac{\frac{5 (- 7 Z \cdot 3 + 67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{\frac{5 (- 7 Z \cdot 3 + 67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $3$ by $- 7$ .

$5 (\frac{\frac{5 (- 21 Z + 67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$5 (\frac{\frac{5 (- 21 Z + 67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $- 1$ out of $- 21 Z$ .

$5 (\frac{\frac{5 (- (21 Z) + 67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Rewrite $67$ as $- 1 (- 67)$ .

$5 (\frac{\frac{5 (- (21 Z) - 1 \cdot - 67 - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $- 1$ out of $- (21 Z) - 1 (- 67)$ .

$5 (\frac{\frac{5 (- (21 Z - 67) - 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $- 1$ out of $- 7 z$ .

$5 (\frac{\frac{5 (- (21 Z - 67) - (7 z))}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $- 1$ out of $- (21 Z - 67) - (7 z)$ .

$5 (\frac{\frac{5 (- (21 Z - 67 + 7 z))}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Rewrite $- (21 Z - 67 + 7 z)$ as $- 1 (21 Z - 67 + 7 z)$ .

$5 (\frac{\frac{5 (- 1 (21 Z - 67 + 7 z))}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Move the negative in front of the fraction.

$5 (\frac{- \frac{5 (21 Z - 67 + 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$5 (\frac{- \frac{5 (21 Z - 67 + 7 z)}{33}}{5}) + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Rewrite the expression.

$- \frac{5 (21 Z - 67 + 7 z)}{33} + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + 7 (\frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Apply the distributive property.

$- \frac{5 (21 Z - 67 + 7 z)}{33} + 7 (\frac{5 Z}{11}) + 7 (- \frac{128}{33}) + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify.

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Multiply $7 \frac{5 Z}{11}$ .

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Combine $7$ and $\frac{5 Z}{11}$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{7 (5 Z)}{11} + 7 (- \frac{128}{33}) + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $5$ by $7$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + 7 (- \frac{128}{33}) + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + 7 (- \frac{128}{33}) + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $7 (- \frac{128}{33})$ .

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Multiply $- 1$ by $7$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} - 7 (\frac{128}{33}) + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine $- 7$ and $\frac{128}{33}$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 7 \cdot 128}{33} + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $- 7$ by $128$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} + 7 (- \frac{28 z}{33}) + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $7 (- \frac{28 z}{33})$ .

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Multiply $- 1$ by $7$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} - 7 \frac{28 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine $- 7$ and $\frac{28 z}{33}$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} + \frac{- 7 (28 z)}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $28$ by $- 7$ .

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} + \frac{- 196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} + \frac{- 196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} + \frac{- 896}{33} + \frac{- 196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify each term.

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Move the negative in front of the fraction.

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} - \frac{896}{33} + \frac{- 196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Move the negative in front of the fraction.

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} - \frac{896}{33} - \frac{196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} - \frac{896}{33} - \frac{196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- \frac{5 (21 Z - 67 + 7 z)}{33} + \frac{35 Z}{11} - \frac{896}{33} - \frac{196 z}{33} + 7 z = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the numerators over the common denominator.

$7 z + \frac{- 5 (21 Z - 67 + 7 z) - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify each term.

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Apply the distributive property.

$7 z + \frac{- 5 (21 Z) - 5 \cdot - 67 - 5 (7 z) - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify.

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Multiply $21$ by $- 5$ .

$7 z + \frac{- 105 Z - 5 \cdot - 67 - 5 (7 z) - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $- 5$ by $- 67$ .

$7 z + \frac{- 105 Z + 335 - 5 (7 z) - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Multiply $7$ by $- 5$ .

$7 z + \frac{- 105 Z + 335 - 35 z - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z + \frac{- 105 Z + 335 - 35 z - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z + \frac{- 105 Z + 335 - 35 z - 896 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Simplify terms.

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Subtract $896$ from $335$ .

$7 z + \frac{- 105 Z - 35 z - 561 - 196 z}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Subtract $196 z$ from $- 35 z$ .

$7 z + \frac{- 105 Z - 231 z - 561}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factor of $- 105 Z - 231 z - 561$ and $33$ .

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Factor $3$ out of $- 105 Z$ .

$7 z + \frac{3 (- 35 Z) - 231 z - 561}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $3$ out of $- 231 z$ .

$7 z + \frac{3 (- 35 Z) + 3 (- 77 z) - 561}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $3$ out of $3 (- 35 Z) + 3 (- 77 z)$ .

$7 z + \frac{3 (- 35 Z - 77 z) - 561}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $3$ out of $- 561$ .

$7 z + \frac{3 (- 35 Z - 77 z) + 3 (- 187)}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $3$ out of $3 (- 35 Z - 77 z) + 3 (- 187)$ .

$7 z + \frac{3 (- 35 Z - 77 z - 187)}{33} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factors.

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Factor $3$ out of $33$ .

$7 z + \frac{3 (- 35 Z - 77 z - 187)}{3 (11)} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factor.

$7 z + \frac{3 (- 35 Z - 77 z - 187)}{3 \cdot 11} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Rewrite the expression.

$7 z + \frac{- 35 Z - 77 z - 187}{11} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z + \frac{- 35 Z - 77 z - 187}{11} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z + \frac{- 35 Z - 77 z - 187}{11} + \frac{35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the numerators over the common denominator.

$7 z + \frac{- 35 Z - 77 z - 187 + 35 Z}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Combine the opposite terms in $- 35 Z - 77 z - 187 + 35 Z$ .

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Add $- 35 Z$ and $35 Z$ .

$7 z + \frac{- 77 z - 187 + 0}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Add $- 77 z - 187$ and $0$ .

$7 z + \frac{- 77 z - 187}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z + \frac{- 77 z - 187}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factor of $- 77 z - 187$ and $11$ .

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Factor $11$ out of $- 77 z$ .

$7 z + \frac{11 (- 7 z) - 187}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $11$ out of $- 187$ .

$7 z + \frac{11 (- 7 z) + 11 \cdot - 17}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Factor $11$ out of $11 (- 7 z) + 11 (- 17)$ .

$7 z + \frac{11 (- 7 z - 17)}{11} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factors.

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Factor $11$ out of $11$ .

$7 z + \frac{11 (- 7 z - 17)}{11 (1)} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Cancel the common factor.

$7 z + \frac{11 (- 7 z - 17)}{11 \cdot 1} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Rewrite the expression.

$7 z + \frac{- 7 z - 17}{1} = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Divide $- 7 z - 17$ by $1$ .

$7 z - 7 z - 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z - 7 z - 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$7 z - 7 z - 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Subtract $7 z$ from $7 z$ .

$0 - 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Subtract $17$ from $0$ .

$- 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

$- 17 = - 17$

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Since $- 17 = - 17$ , the equation will always be true.

Always true

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Always true

$y = \frac{5 Z}{11} - \frac{128}{33} - \frac{28 z}{33}$

Step 4

Simplify the right side.

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Move $- \frac{128}{33}$ .

$y = \frac{5 Z}{11} - \frac{28 z}{33} - \frac{128}{33}$

Always true

$y = \frac{5 Z}{11} - \frac{28 z}{33} - \frac{128}{33}$

Always true