Pre-Algebra Examples

$7 = - \frac{3}{4} x - 2$

Step 1

Solve for $y$ .

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Step 1.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- \frac{3 x}{4} - 2 = 7$

Step 1.2

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

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Step 1.2.1

Add $2$ to both sides of the equation.

$- \frac{3 x}{4} = 7 + 2$

Step 1.2.2

Add $7$ and $2$ .

$- \frac{3 x}{4} = 9$

Step 1.3

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot 9$

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

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Step 1.4.1.1.1

Cancel the common factor of $4$ .

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Step 1.4.1.1.1.1

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

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.1.2

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

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.2

Cancel the common factor of $3$ .

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Step 1.4.1.1.2.1

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.3

Multiply.

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Step 1.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} \cdot 9$

Step 1.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{4}{3} \cdot 9$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $- \frac{4}{3} \cdot 9$ .

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Step 1.4.2.1.1

Cancel the common factor of $3$ .

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Step 1.4.2.1.1.1

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

$x = \frac{- 4}{3} \cdot 9$

Step 1.4.2.1.1.2

Factor $3$ out of $9$ .

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

Step 1.4.2.1.1.3

Cancel the common factor.

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

Step 1.4.2.1.1.4

Rewrite the expression.

$x = - 4 \cdot 3$

Step 1.4.2.1.2

Multiply $- 4$ by $3$ .

$x = - 12$

Step 2

Since $x = - 12$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ - 12 & 0 \\ - 12 & 1 \end{array}$

Step 4

Graph the line using the slope, y-intercept, and two points.

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ - 12 & 0 \\ - 12 & 1 \end{array}$

Step 5