Solve the Absolute Value Inequality for x 2|3x-5|-8=8

$2 | 3 x - 5 | - 8 = 8$

Step 1

Move all terms not containing $| 3 x - 5 |$ to the right side of the equation.

Add $8$ to both sides of the equation.

$2 | 3 x - 5 | = 8 + 8$

Add $8$ and $8$ .

$2 | 3 x - 5 | = 16$

Step 2

Divide each term in $2 | 3 x - 5 | = 16$ by $2$ and simplify.

Divide each term in $2 | 3 x - 5 | = 16$ by $2$ .

$\frac{2 | 3 x - 5 |}{2} = \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | 3 x - 5 |}{2} = \frac{16}{2}$

Divide $| 3 x - 5 |$ by $1$ .

$| 3 x - 5 | = \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$| 3 x - 5 | = 8$

Step 3

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

$3 x - 5 = \pm 8$

Step 4

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

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

$3 x - 5 = 8$

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

Add $5$ to both sides of the equation.

$3 x = 8 + 5$

Add $8$ and $5$ .

$3 x = 13$

Divide each term in $3 x = 13$ by $3$ and simplify.

Divide each term in $3 x = 13$ by $3$ .

$\frac{3 x}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{13}{3}$

Divide $x$ by $1$ .

$x = \frac{13}{3}$

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

$3 x - 5 = - 8$

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

Add $5$ to both sides of the equation.

$3 x = - 8 + 5$

Add $- 8$ and $5$ .

$3 x = - 3$

Divide each term in $3 x = - 3$ by $3$ and simplify.

Divide each term in $3 x = - 3$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $3$ .

$x = - 1$

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

$x = \frac{13}{3}, - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{3}, - 1$

Decimal Form:

$x = 4.\overline{3}, - 1$

Mixed Number Form:

$x = 4 \frac{1}{3}, - 1$

Solve the Absolute Value Inequality for x 2|3x-5|-8=8

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