Finite Math Examples

$- \frac{2}{7} x + \frac{6}{7} y - \frac{5}{7} z = 0$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{2}{7}$ .

$- \frac{x \cdot 2}{7} + \frac{6}{7} y - \frac{5}{7} z = 0$

Step 1.2

Move $2$ to the left of $x$ .

$- \frac{2 \cdot x}{7} + \frac{6}{7} y - \frac{5}{7} z = 0$

Step 1.3

Combine $\frac{6}{7}$ and $y$ .

$- \frac{2 x}{7} + \frac{6 y}{7} - \frac{5}{7} z = 0$

Step 1.4

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

$- \frac{2 x}{7} + \frac{6 y}{7} - \frac{z \cdot 5}{7} = 0$

Step 1.5

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

$- \frac{2 x}{7} + \frac{6 y}{7} - \frac{5 z}{7} = 0$

Step 2

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

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Step 2.1

Add $\frac{2 x}{7}$ to both sides of the equation.

$\frac{6 y}{7} - \frac{5 z}{7} = \frac{2 x}{7}$

Step 2.2

Subtract $\frac{6 y}{7}$ from both sides of the equation.

$- \frac{5 z}{7} = \frac{2 x}{7} - \frac{6 y}{7}$

Step 3

Multiply both sides of the equation by $- \frac{7}{5}$ .

$- \frac{7}{5} (- \frac{5 z}{7}) = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$\frac{- 7}{5} (- \frac{5 z}{7}) = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{5 z}{7}$ into the numerator.

$\frac{- 7}{5} \cdot \frac{- 5 z}{7} = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{5} \cdot \frac{- 5 z}{7} = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{5} \cdot \frac{- 5 z}{7} = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 z) = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

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

$\frac{- 1}{5} (5 (- z)) = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- z)) = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.2.3

Rewrite the expression.

$- - z = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{7}{5} (\frac{2 x}{7} - \frac{6 y}{7})$ .

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Step 4.2.1.1

Apply the distributive property.

$z = - \frac{7}{5} \cdot \frac{2 x}{7} - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.2

Cancel the common factor of $7$ .

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Step 4.2.1.2.1

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$z = \frac{- 7}{5} \cdot \frac{2 x}{7} - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.2.2

Factor $7$ out of $- 7$ .

$z = \frac{7 (- 1)}{5} \cdot \frac{2 x}{7} - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.2.3

Cancel the common factor.

$z = \frac{7 \cdot - 1}{5} \cdot \frac{2 x}{7} - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.2.4

Rewrite the expression.

$z = \frac{- 1}{5} (2 x) - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.3

Combine $2$ and $\frac{- 1}{5}$ .

$z = \frac{2 \cdot - 1}{5} x - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.4

Multiply $2$ by $- 1$ .

$z = \frac{- 2}{5} x - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.5

Combine $\frac{- 2}{5}$ and $x$ .

$z = \frac{- 2 x}{5} - \frac{7}{5} (- \frac{6 y}{7})$

Step 4.2.1.6

Cancel the common factor of $7$ .

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Step 4.2.1.6.1

Move the leading negative in $- \frac{7}{5}$ into the numerator.

$z = \frac{- 2 x}{5} + \frac{- 7}{5} (- \frac{6 y}{7})$

Step 4.2.1.6.2

Move the leading negative in $- \frac{6 y}{7}$ into the numerator.

$z = \frac{- 2 x}{5} + \frac{- 7}{5} \cdot \frac{- 6 y}{7}$

Step 4.2.1.6.3

Factor $7$ out of $- 7$ .

$z = \frac{- 2 x}{5} + \frac{7 (- 1)}{5} \cdot \frac{- 6 y}{7}$

Step 4.2.1.6.4

Cancel the common factor.

$z = \frac{- 2 x}{5} + \frac{7 \cdot - 1}{5} \cdot \frac{- 6 y}{7}$

Step 4.2.1.6.5

Rewrite the expression.

$z = \frac{- 2 x}{5} + \frac{- 1}{5} (- 6 y)$

Step 4.2.1.7

Combine $- 6$ and $\frac{- 1}{5}$ .

$z = \frac{- 2 x}{5} + \frac{- 6 \cdot - 1}{5} y$

Step 4.2.1.8

Multiply $- 6$ by $- 1$ .

$z = \frac{- 2 x}{5} + \frac{6}{5} y$

Step 4.2.1.9

Combine $\frac{6}{5}$ and $y$ .

$z = \frac{- 2 x}{5} + \frac{6 y}{5}$

Step 4.2.1.10

Move the negative in front of the fraction.

$z = - \frac{2 x}{5} + \frac{6 y}{5}$