Pre-Algebra Examples

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

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Step 1.1.2

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

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

Step 1.1.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.1.4.1

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

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

Step 1.1.4.2

Multiply $3$ by $2$ .

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

Step 1.1.4.3

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

$2 x = \frac{2 \cdot 2}{6} - \frac{3}{2 \cdot 3}$

Step 1.1.4.4

Multiply $2$ by $3$ .

$2 x = \frac{2 \cdot 2}{6} - \frac{3}{6}$

Step 1.1.5

Combine the numerators over the common denominator.

$2 x = \frac{2 \cdot 2 - 3}{6}$

Step 1.1.6

Simplify the numerator.

Tap for more steps...

Step 1.1.6.1

Multiply $2$ by $2$ .

$2 x = \frac{4 - 3}{6}$

Step 1.1.6.2

Subtract $3$ from $4$ .

$2 x = \frac{1}{6}$

Step 1.2

Divide each term in $2 x = \frac{1}{6}$ by $2$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $2 x = \frac{1}{6}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{1}{6}}{2}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{1}{6}}{2}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{6}}{2}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{6} \cdot \frac{1}{2}$

Step 1.2.3.2

Multiply $\frac{1}{6} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 1.2.3.2.1

Multiply $\frac{1}{6}$ by $\frac{1}{2}$ .

$x = \frac{1}{6 \cdot 2}$

Step 1.2.3.2.2

Multiply $6$ by $2$ .

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

Step 2

Since $x = \frac{1}{12}$ 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.

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

Step 4

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

Slope: Undefined

y-intercept: No y-intercept

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

Step 5