Pre-Algebra Examples

$\frac{x}{3} - 1 = - \frac{13}{12}$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Add $1$ to both sides of the equation.

$\frac{x}{3} = - \frac{13}{12} + 1$

Step 1.1.2

Write $1$ as a fraction with a common denominator.

$\frac{x}{3} = - \frac{13}{12} + \frac{12}{12}$

Step 1.1.3

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{- 13 + 12}{12}$

Step 1.1.4

Add $- 13$ and $12$ .

$\frac{x}{3} = \frac{- 1}{12}$

Step 1.1.5

Move the negative in front of the fraction.

$\frac{x}{3} = - \frac{1}{12}$

Step 1.2

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (- \frac{1}{12})$

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 (- \frac{1}{12})$

Step 1.3.1.1.2

Rewrite the expression.

$x = 3 (- \frac{1}{12})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $3 (- \frac{1}{12})$ .

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Step 1.3.2.1.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1.1

Move the leading negative in $- \frac{1}{12}$ into the numerator.

$x = 3 (\frac{- 1}{12})$

Step 1.3.2.1.1.2

Factor $3$ out of $12$ .

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

Step 1.3.2.1.1.3

Cancel the common factor.

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

Step 1.3.2.1.1.4

Rewrite the expression.

$x = \frac{- 1}{4}$

Step 1.3.2.1.2

Move the negative in front of the fraction.

$x = - \frac{1}{4}$

Step 2

Since $x = - \frac{1}{4}$ 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.

$\begin{array}{c} x & y \\ - \frac{1}{4} & 0 \\ - \frac{1}{4} & 1 \end{array}$

Step 4

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

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ - \frac{1}{4} & 0 \\ - \frac{1}{4} & 1 \end{array}$

Step 5