Algebra Examples

$\frac{| 12 - x |}{2} = 4 x$

Step 1

Multiply both sides by $2$ .

$\frac{| 12 - x |}{2} \cdot 2 = 4 x \cdot 2$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor.

$\frac{| 12 - x |}{2} \cdot 2 = 4 x \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$| 12 - x | = 4 x \cdot 2$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Multiply $2$ by $4$ .

$| 12 - x | = 8 x$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

$12 - x = \pm 8 x$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$12 - x = 8 x$

Step 3.2.2

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.2.2.1

Subtract $8 x$ from both sides of the equation.

$12 - x - 8 x = 0$

Step 3.2.2.2

Subtract $8 x$ from $- x$ .

$12 - 9 x = 0$

Step 3.2.3

Subtract $12$ from both sides of the equation.

$- 9 x = - 12$

Step 3.2.4

Divide each term in $- 9 x = - 12$ by $- 9$ and simplify.

Tap for more steps...

Step 3.2.4.1

Divide each term in $- 9 x = - 12$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 12}{- 9}$

Step 3.2.4.2

Simplify the left side.

Tap for more steps...

Step 3.2.4.2.1

Cancel the common factor of $- 9$ .

Tap for more steps...

Step 3.2.4.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 12}{- 9}$

Step 3.2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 9}$

Step 3.2.4.3

Simplify the right side.

Tap for more steps...

Step 3.2.4.3.1

Cancel the common factor of $- 12$ and $- 9$ .

Tap for more steps...

Step 3.2.4.3.1.1

Factor $- 3$ out of $- 12$ .

$x = \frac{- 3 (4)}{- 9}$

Step 3.2.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.2.4.3.1.2.1

Factor $- 3$ out of $- 9$ .

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

Step 3.2.4.3.1.2.2

Cancel the common factor.

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

Step 3.2.4.3.1.2.3

Rewrite the expression.

$x = \frac{4}{3}$

Step 3.2.5

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

$12 - x = - 8 x$

Step 3.2.6

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.2.6.1

Add $8 x$ to both sides of the equation.

$12 - x + 8 x = 0$

Step 3.2.6.2

Add $- x$ and $8 x$ .

$12 + 7 x = 0$

Step 3.2.7

Subtract $12$ from both sides of the equation.

$7 x = - 12$

Step 3.2.8

Divide each term in $7 x = - 12$ by $7$ and simplify.

Tap for more steps...

Step 3.2.8.1

Divide each term in $7 x = - 12$ by $7$ .

$\frac{7 x}{7} = \frac{- 12}{7}$

Step 3.2.8.2

Simplify the left side.

Tap for more steps...

Step 3.2.8.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 3.2.8.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 12}{7}$

Step 3.2.8.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{7}$

Step 3.2.8.3

Simplify the right side.

Tap for more steps...

Step 3.2.8.3.1

Move the negative in front of the fraction.

$x = - \frac{12}{7}$

Step 3.2.9

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

$x = \frac{4}{3}, - \frac{12}{7}$

Step 4

Exclude the solutions that do not make $\frac{| 12 - x |}{2} = 4 x$ true.

$x = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}$

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

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