Pre-Algebra Examples

$y - 4 = - \frac{9}{8} \cdot (x + 5)$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $8$ .

$8 (y - 4) = 8 (- \frac{9}{8} \cdot (x + 5))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $8 (y - 4)$ .

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Step 3.1.1

Apply the distributive property.

$8 y + 8 \cdot - 4 = 8 (- \frac{9}{8} \cdot (x + 5))$

Step 3.1.2

Multiply $8$ by $- 4$ .

$8 y - 32 = 8 (- \frac{9}{8} \cdot (x + 5))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $8 (- \frac{9}{8} \cdot (x + 5))$ .

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Step 4.1.1

Apply the distributive property.

$8 y - 32 = 8 (- \frac{9}{8} x - \frac{9}{8} \cdot 5)$

Step 4.1.2

Combine $x$ and $\frac{9}{8}$ .

$8 y - 32 = 8 (- \frac{x \cdot 9}{8} - \frac{9}{8} \cdot 5)$

Step 4.1.3

Multiply $- \frac{9}{8} \cdot 5$ .

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Step 4.1.3.1

Multiply $5$ by $- 1$ .

$8 y - 32 = 8 (- \frac{x \cdot 9}{8} - 5 (\frac{9}{8}))$

Step 4.1.3.2

Combine $- 5$ and $\frac{9}{8}$ .

$8 y - 32 = 8 (- \frac{x \cdot 9}{8} + \frac{- 5 \cdot 9}{8})$

Step 4.1.3.3

Multiply $- 5$ by $9$ .

$8 y - 32 = 8 (- \frac{x \cdot 9}{8} + \frac{- 45}{8})$

Step 4.1.4

Simplify each term.

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Step 4.1.4.1

Move $9$ to the left of $x$ .

$8 y - 32 = 8 (- \frac{9 \cdot x}{8} + \frac{- 45}{8})$

Step 4.1.4.2

Move the negative in front of the fraction.

$8 y - 32 = 8 (- \frac{9 x}{8} - \frac{45}{8})$

Step 4.1.5

Simplify terms.

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Step 4.1.5.1

Apply the distributive property.

$8 y - 32 = 8 (- \frac{9 x}{8}) + 8 (- \frac{45}{8})$

Step 4.1.5.2

Cancel the common factor of $8$ .

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Step 4.1.5.2.1

Move the leading negative in $- \frac{9 x}{8}$ into the numerator.

$8 y - 32 = 8 \frac{- 9 x}{8} + 8 (- \frac{45}{8})$

Step 4.1.5.2.2

Cancel the common factor.

$8 y - 32 = 8 \frac{- 9 x}{8} + 8 (- \frac{45}{8})$

Step 4.1.5.2.3

Rewrite the expression.

$8 y - 32 = - 9 x + 8 (- \frac{45}{8})$

Step 4.1.5.3

Cancel the common factor of $8$ .

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Step 4.1.5.3.1

Move the leading negative in $- \frac{45}{8}$ into the numerator.

$8 y - 32 = - 9 x + 8 (\frac{- 45}{8})$

Step 4.1.5.3.2

Cancel the common factor.

$8 y - 32 = - 9 x + 8 (\frac{- 45}{8})$

Step 4.1.5.3.3

Rewrite the expression.

$8 y - 32 = - 9 x - 45$

Step 5

Move all terms containing variables to the left side of the equation.

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Step 5.1

Add $9 x$ to both sides of the equation.

$8 y - 32 + 9 x = - 45$

Step 5.2

Move $- 32$ .

$8 y + 9 x - 32 = - 45$

Step 5.3

Reorder $8 y$ and $9 x$ .

$9 x + 8 y - 32 = - 45$

Step 6

Move all terms not containing a variable to the right side of the equation.

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Step 6.1

Add $32$ to both sides of the equation.

$9 x + 8 y = - 45 + 32$

Step 6.2

Add $- 45$ and $32$ .

$9 x + 8 y = - 13$

Step 7