Pre-Algebra Examples

$2 x - \frac{1}{3} = - 2$

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 $\frac{1}{3}$ to both sides of the equation.

$2 x = - 2 + \frac{1}{3}$

Step 1.1.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 x = - 2 \cdot \frac{3}{3} + \frac{1}{3}$

Step 1.1.3

Combine $- 2$ and $\frac{3}{3}$ .

$2 x = \frac{- 2 \cdot 3}{3} + \frac{1}{3}$

Step 1.1.4

Combine the numerators over the common denominator.

$2 x = \frac{- 2 \cdot 3 + 1}{3}$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Multiply $- 2$ by $3$ .

$2 x = \frac{- 6 + 1}{3}$

Step 1.1.5.2

Add $- 6$ and $1$ .

$2 x = \frac{- 5}{3}$

Step 1.1.6

Move the negative in front of the fraction.

$2 x = - \frac{5}{3}$

Step 1.2

Divide each term in $2 x = - \frac{5}{3}$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = - \frac{5}{3}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{5}{3}}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \frac{5}{3}}{2}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{5}{3}}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{5}{3} \cdot \frac{1}{2}$

Step 1.2.3.2

Multiply $- \frac{5}{3} \cdot \frac{1}{2}$ .

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Step 1.2.3.2.1

Multiply $\frac{1}{2}$ by $\frac{5}{3}$ .

$x = - \frac{5}{2 \cdot 3}$

Step 1.2.3.2.2

Multiply $2$ by $3$ .

$x = - \frac{5}{6}$

Step 2

Since $x = - \frac{5}{6}$ 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.

$\begin{array}{c} x & y \\ - \frac{5}{6} & 0 \\ - \frac{5}{6} & 1 \end{array}$

Step 4

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

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ - \frac{5}{6} & 0 \\ - \frac{5}{6} & 1 \end{array}$

Step 5