Solve the Absolute Value Inequality for x |3x-4|=5

$| 3 x - 4 | = 5$

Step 1

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

$3 x - 4 = \pm 5$

Step 2

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.

$3 x - 4 = 5$

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

Add $4$ to both sides of the equation.

$3 x = 5 + 4$

Add $5$ and $4$ .

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

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

$3 x - 4 = - 5$

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

Add $4$ to both sides of the equation.

$3 x = - 5 + 4$

Add $- 5$ and $4$ .

$3 x = - 1$

Divide each term in $3 x = - 1$ by $3$ and simplify.

Divide each term in $3 x = - 1$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 3, - 0.\overline{3}$

Solve the Absolute Value Inequality for x |3x-4|=5

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