Finite Math Examples

$y = 4 (\frac{x - 7}{- 3}) + 5$

Step 1

Rewrite the equation as $4 (\frac{x - 7}{- 3}) + 5 = y$ .

$4 (\frac{x - 7}{- 3}) + 5 = y$

Step 2

Simplify $4 (\frac{x - 7}{- 3}) + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Move the negative in front of the fraction.

$4 (- \frac{x - 7}{3}) + 5 = y$

Step 2.1.2

Multiply $4 (- \frac{x - 7}{3})$ .

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Step 2.1.2.1

Multiply $- 1$ by $4$ .

$- 4 \frac{x - 7}{3} + 5 = y$

Step 2.1.2.2

Combine $- 4$ and $\frac{x - 7}{3}$ .

$\frac{- 4 (x - 7)}{3} + 5 = y$

Step 2.1.3

Move the negative in front of the fraction.

$- \frac{4 (x - 7)}{3} + 5 = y$

Step 2.2

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

$- \frac{4 (x - 7)}{3} + 5 \cdot \frac{3}{3} = y$

Step 2.3

Simplify terms.

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Step 2.3.1

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

$- \frac{4 (x - 7)}{3} + \frac{5 \cdot 3}{3} = y$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{- 4 (x - 7) + 5 \cdot 3}{3} = y$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Apply the distributive property.

$\frac{- 4 x - 4 \cdot - 7 + 5 \cdot 3}{3} = y$

Step 2.4.2

Multiply $- 4$ by $- 7$ .

$\frac{- 4 x + 28 + 5 \cdot 3}{3} = y$

Step 2.4.3

Multiply $5$ by $3$ .

$\frac{- 4 x + 28 + 15}{3} = y$

Step 2.4.4

Add $28$ and $15$ .

$\frac{- 4 x + 43}{3} = y$

Step 2.5

Simplify with factoring out.

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Step 2.5.1

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) + 43}{3} = y$

Step 2.5.2

Rewrite $43$ as $- 1 (- 43)$ .

$\frac{- (4 x) - 1 (- 43)}{3} = y$

Step 2.5.3

Factor $- 1$ out of $- (4 x) - 1 (- 43)$ .

$\frac{- (4 x - 43)}{3} = y$

Step 2.5.4

Simplify the expression.

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Step 2.5.4.1

Rewrite $- (4 x - 43)$ as $- 1 (4 x - 43)$ .

$\frac{- 1 (4 x - 43)}{3} = y$

Step 2.5.4.2

Move the negative in front of the fraction.

$- \frac{4 x - 43}{3} = y$

Step 3

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{4 x - 43}{3}) = - 3 y$

Step 4

Simplify the left side.

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Step 4.1

Simplify $- 3 (- \frac{4 x - 43}{3})$ .

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Move the leading negative in $- \frac{4 x - 43}{3}$ into the numerator.

$- 3 \frac{- (4 x - 43)}{3} = - 3 y$

Step 4.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- (4 x - 43)}{3} = - 3 y$

Step 4.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- (4 x - 43)}{3} = - 3 y$

Step 4.1.1.4

Rewrite the expression.

$- - (4 x - 43) = - 3 y$

Step 4.1.2

Multiply.

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Step 4.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (4 x - 43) = - 3 y$

Step 4.1.2.2

Multiply $4 x - 43$ by $1$ .

$4 x - 43 = - 3 y$

Step 5

Add $43$ to both sides of the equation.

$4 x = - 3 y + 43$

Step 6

Divide each term in $4 x = - 3 y + 43$ by $4$ and simplify.

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Step 6.1

Divide each term in $4 x = - 3 y + 43$ by $4$ .

$\frac{4 x}{4} = \frac{- 3 y}{4} + \frac{43}{4}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3 y}{4} + \frac{43}{4}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3 y}{4} + \frac{43}{4}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{3 y}{4} + \frac{43}{4}$