Pre-Algebra Examples

$\frac{x + y}{- 5} + 7 = - 12$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $\frac{x + y}{- 5} + 7$ .

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Step 1.2.1.1

Move the negative in front of the fraction.

$- \frac{x + y}{5} + 7 = - 12$

Step 1.2.1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{x + y}{5} + 7 \cdot \frac{5}{5} = - 12$

Step 1.2.1.3

Simplify terms.

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Step 1.2.1.3.1

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

$- \frac{x + y}{5} + \frac{7 \cdot 5}{5} = - 12$

Step 1.2.1.3.2

Combine the numerators over the common denominator.

$\frac{- (x + y) + 7 \cdot 5}{5} = - 12$

Step 1.2.1.4

Simplify the numerator.

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Step 1.2.1.4.1

Apply the distributive property.

$\frac{- x - y + 7 \cdot 5}{5} = - 12$

Step 1.2.1.4.2

Multiply $7$ by $5$ .

$\frac{- x - y + 35}{5} = - 12$

Step 1.2.1.5

Simplify with factoring out.

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Step 1.2.1.5.1

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

$\frac{- (x) - y + 35}{5} = - 12$

Step 1.2.1.5.2

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

$\frac{- (x) - (y) + 35}{5} = - 12$

Step 1.2.1.5.3

Factor $- 1$ out of $- (x) - (y)$ .

$\frac{- (x + y) + 35}{5} = - 12$

Step 1.2.1.5.4

Rewrite $35$ as $- 1 (- 35)$ .

$\frac{- (x + y) - 1 (- 35)}{5} = - 12$

Step 1.2.1.5.5

Factor $- 1$ out of $- (x + y) - 1 (- 35)$ .

$\frac{- (x + y - 35)}{5} = - 12$

Step 1.2.1.5.6

Simplify the expression.

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Step 1.2.1.5.6.1

Rewrite $- (x + y - 35)$ as $- 1 (x + y - 35)$ .

$\frac{- 1 (x + y - 35)}{5} = - 12$

Step 1.2.1.5.6.2

Move the negative in front of the fraction.

$- \frac{x + y - 35}{5} = - 12$

Step 1.3

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

$- 5 (- \frac{x + y - 35}{5}) = - 5 \cdot - 12$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $- 5 (- \frac{x + y - 35}{5})$ .

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Step 1.4.1.1.1

Cancel the common factor of $5$ .

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Step 1.4.1.1.1.1

Move the leading negative in $- \frac{x + y - 35}{5}$ into the numerator.

$- 5 \frac{- (x + y - 35)}{5} = - 5 \cdot - 12$

Step 1.4.1.1.1.2

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{- (x + y - 35)}{5} = - 5 \cdot - 12$

Step 1.4.1.1.1.3

Cancel the common factor.

$5 \cdot - 1 \frac{- (x + y - 35)}{5} = - 5 \cdot - 12$

Step 1.4.1.1.1.4

Rewrite the expression.

$- - (x + y - 35) = - 5 \cdot - 12$

Step 1.4.1.1.2

Multiply.

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Step 1.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (x + y - 35) = - 5 \cdot - 12$

Step 1.4.1.1.2.2

Multiply $x + y - 35$ by $1$ .

$x + y - 35 = - 5 \cdot - 12$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Multiply $- 5$ by $- 12$ .

$x + y - 35 = 60$

Step 1.5

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

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Step 1.5.1

Subtract $x$ from both sides of the equation.

$y - 35 = 60 - x$

Step 1.5.2

Add $35$ to both sides of the equation.

$y = 60 - x + 35$

Step 1.5.3

Add $60$ and $35$ .

$y = - x + 95$

Step 2

Using the slope-intercept form, the slope is $- 1$ .

$m = - 1$

Step 3