Solve for x |2-3x|=11

$| 2 - 3 x | = 11$

Step 1

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

$2 - 3 x = \pm 11$

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.

$2 - 3 x = 11$

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

Subtract $2$ from both sides of the equation.

$- 3 x = 11 - 2$

Subtract $2$ from $11$ .

$- 3 x = 9$

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.

$2 - 3 x = - 11$

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

Subtract $2$ from both sides of the equation.

$- 3 x = - 11 - 2$

Subtract $2$ from $- 11$ .

$- 3 x = - 13$

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 $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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

Mixed Number Form:

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

Solve for x |2-3x|=11

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