Pre-Algebra Examples

$\frac{1}{5} x + 2 = \frac{11}{3}$

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

Subtract $2$ from both sides of the equation.

$\frac{x}{5} = \frac{11}{3} - 2$

Step 1.1.2

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

$\frac{x}{5} = \frac{11}{3} - 2 \cdot \frac{3}{3}$

Step 1.1.3

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

$\frac{x}{5} = \frac{11}{3} + \frac{- 2 \cdot 3}{3}$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{x}{5} = \frac{11 - 2 \cdot 3}{3}$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Multiply $- 2$ by $3$ .

$\frac{x}{5} = \frac{11 - 6}{3}$

Step 1.1.5.2

Subtract $6$ from $11$ .

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

Step 1.2

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 (\frac{5}{3})$

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 $5$ .

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Step 1.3.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 (\frac{5}{3})$

Step 1.3.1.1.2

Rewrite the expression.

$x = 5 (\frac{5}{3})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Multiply $5 (\frac{5}{3})$ .

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Step 1.3.2.1.1

Combine $5$ and $\frac{5}{3}$ .

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

Step 1.3.2.1.2

Multiply $5$ by $5$ .

$x = \frac{25}{3}$

Step 2

Since $x = \frac{25}{3}$ 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.

$\begin{array}{c} x & y \\ \frac{25}{3} & 0 \\ \frac{25}{3} & 1 \end{array}$

Step 4

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

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ \frac{25}{3} & 0 \\ \frac{25}{3} & 1 \end{array}$

Step 5