Pre-Algebra Examples

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

Step 1

The absolute value is the distance between a number and zero. The distance between $- 3$ and $0$ is $3$ .

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

Step 2

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

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

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

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

Step 3.2

Multiply both sides by $3$ .

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

Step 3.3

Simplify.

Tap for more steps...

Step 3.3.1

Simplify the left side.

Tap for more steps...

Step 3.3.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.1.1.1

Cancel the common factor.

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

Step 3.3.1.1.2

Rewrite the expression.

$2 x - 1 = 3 \cdot 3$

Step 3.3.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.1

Multiply $3$ by $3$ .

$2 x - 1 = 9$

Step 3.4

Solve for $x$ .

Tap for more steps...

Step 3.4.1

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

Tap for more steps...

Step 3.4.1.1

Add $1$ to both sides of the equation.

$2 x = 9 + 1$

Step 3.4.1.2

Add $9$ and $1$ .

$2 x = 10$

Step 3.4.2

Divide each term in $2 x = 10$ by $2$ and simplify.

Tap for more steps...

Step 3.4.2.1

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Step 3.4.2.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Step 3.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Step 3.4.2.3

Simplify the right side.

Tap for more steps...

Step 3.4.2.3.1

Divide $10$ by $2$ .

$x = 5$

Step 3.5

Next, use the negative value of the $\pm$ to find the second solution.

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

Step 3.6

Multiply both sides by $3$ .

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

Step 3.7

Simplify.

Tap for more steps...

Step 3.7.1

Simplify the left side.

Tap for more steps...

Step 3.7.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.7.1.1.1

Cancel the common factor.

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

Step 3.7.1.1.2

Rewrite the expression.

$2 x - 1 = - 3 \cdot 3$

Step 3.7.2

Simplify the right side.

Tap for more steps...

Step 3.7.2.1

Multiply $- 3$ by $3$ .

$2 x - 1 = - 9$

Step 3.8

Solve for $x$ .

Tap for more steps...

Step 3.8.1

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

Tap for more steps...

Step 3.8.1.1

Add $1$ to both sides of the equation.

$2 x = - 9 + 1$

Step 3.8.1.2

Add $- 9$ and $1$ .

$2 x = - 8$

Step 3.8.2

Divide each term in $2 x = - 8$ by $2$ and simplify.

Tap for more steps...

Step 3.8.2.1

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 3.8.2.2

Simplify the left side.

Tap for more steps...

Step 3.8.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.8.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 3.8.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Step 3.8.2.3

Simplify the right side.

Tap for more steps...

Step 3.8.2.3.1

Divide $- 8$ by $2$ .

$x = - 4$

Step 3.9

The complete solution is the result of both the positive and negative portions of the solution.

$x = 5, - 4$