Pre-Algebra Examples

$y - 5 = 8 (x + 40)$

Step 1

Rewrite the equation as $8 (x + 40) = y - 5$ .

$8 (x + 40) = y - 5$

Step 2

Divide each term in $8 (x + 40) = y - 5$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 (x + 40) = y - 5$ by $8$ .

$\frac{8 (x + 40)}{8} = \frac{y}{8} + \frac{- 5}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 (x + 40)}{8} = \frac{y}{8} + \frac{- 5}{8}$

Step 2.2.1.2

Divide $x + 40$ by $1$ .

$x + 40 = \frac{y}{8} + \frac{- 5}{8}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$x + 40 = \frac{y}{8} - \frac{5}{8}$

Step 3

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

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Step 3.1

Subtract $40$ from both sides of the equation.

$x = \frac{y}{8} - \frac{5}{8} - 40$

Step 3.2

To write $- 40$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x = \frac{y}{8} - \frac{5}{8} - 40 \cdot \frac{8}{8}$

Step 3.3

Combine $- 40$ and $\frac{8}{8}$ .

$x = \frac{y}{8} - \frac{5}{8} + \frac{- 40 \cdot 8}{8}$

Step 3.4

Combine the numerators over the common denominator.

$x = \frac{y}{8} + \frac{- 5 - 40 \cdot 8}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 40$ by $8$ .

$x = \frac{y}{8} + \frac{- 5 - 320}{8}$

Step 3.5.2

Subtract $320$ from $- 5$ .

$x = \frac{y}{8} + \frac{- 325}{8}$

Step 3.6

Move the negative in front of the fraction.

$x = \frac{y}{8} - \frac{325}{8}$