Solve the Absolute Value Inequality for x 2|3x-2|=14

$2 | 3 x - 2 | = 14$

Divide each term in $2 | 3 x - 2 | = 14$ by $2$ and simplify.

Divide each term in $2 | 3 x - 2 | = 14$ by $2$ .

$\frac{2 | 3 x - 2 |}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | 3 x - 2 |}{2} = \frac{14}{2}$

Divide $| 3 x - 2 |$ by $1$ .

$| 3 x - 2 | = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$| 3 x - 2 | = 7$

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

$3 x - 2 = \pm 7$

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.

$3 x - 2 = 7$

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

Add $2$ to both sides of the equation.

$3 x = 7 + 2$

Add $7$ and $2$ .

$3 x = 9$

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.

$3 x - 2 = - 7$

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

Add $2$ to both sides of the equation.

$3 x = - 7 + 2$

Add $- 7$ and $2$ .

$3 x = - 5$

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

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

$\frac{3 x}{3} = \frac{- 5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 5}{3}$

Divide $x$ by $1$ .

$x = \frac{- 5}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

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

$x = 3, - \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = 3, - \frac{5}{3}$

Decimal Form:

$x = 3, - 1.\overline{6}$

Mixed Number Form:

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

Solve the Absolute Value Inequality for x 2|3x-2|=14

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