Solve the Absolute Value Inequality for x |-3x+6|=2

$| - 3 x + 6 | = 2$

Step 1

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

$- 3 x + 6 = \pm 2$

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.

$- 3 x + 6 = 2$

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

Subtract $6$ from both sides of the equation.

$- 3 x = 2 - 6$

Subtract $6$ from $2$ .

$- 3 x = - 4$

Divide each term in $- 3 x = - 4$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 4$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{4}{3}$

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

$- 3 x + 6 = - 2$

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

Subtract $6$ from both sides of the equation.

$- 3 x = - 2 - 6$

Subtract $6$ from $- 2$ .

$- 3 x = - 8$

Divide each term in $- 3 x = - 8$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 8$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 8}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 8}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{8}{3}$

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

$x = \frac{4}{3}, \frac{8}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{3}, \frac{8}{3}$

Decimal Form:

$x = 1.\overline{3}, 2.\overline{6}$

Mixed Number Form:

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

Solve the Absolute Value Inequality for x |-3x+6|=2

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