Solve for x |3x-2|=5

$| 3 x - 2 | = 5$

Step 1

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

$3 x - 2 = \pm 5$

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.

$3 x - 2 = 5$

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

Add $2$ to both sides of the equation.

$3 x = 5 + 2$

Add $5$ and $2$ .

$3 x = 7$

Divide each term in $3 x = 7$ by $3$ and simplify.

Divide each term in $3 x = 7$ by $3$ .

$\frac{3 x}{3} = \frac{7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{7}{3}$

Divide $x$ by $1$ .

$x = \frac{7}{3}$

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

$3 x - 2 = - 5$

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

Add $2$ to both sides of the equation.

$3 x = - 5 + 2$

Add $- 5$ and $2$ .

$3 x = - 3$

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.

$x = \frac{7}{3}, - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{3}, - 1$

Decimal Form:

$x = 2.\overline{3}, - 1$

Mixed Number Form:

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

Solve for x |3x-2|=5

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