Solve for x |3x-1|=2

$| 3 x - 1 | = 2$

Step 1

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

$3 x - 1 = \pm 2$

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.

$3 x - 1 = 2$

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

Add $1$ to both sides of the equation.

$3 x = 2 + 1$

Add $2$ and $1$ .

$3 x = 3$

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 $3$ .

$x = 1$

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

$3 x - 1 = - 2$

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

Add $1$ to both sides of the equation.

$3 x = - 2 + 1$

Add $- 2$ and $1$ .

$3 x = - 1$

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.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1, - 0.\overline{3}$

Solve for x |3x-1|=2

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