Solve the Absolute Value Inequality for x 8+|6-4x|=17

$8 + | 6 - 4 x | = 17$

Move all terms not containing $| 6 - 4 x |$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$| 6 - 4 x | = 17 - 8$

Subtract $8$ from $17$ .

$| 6 - 4 x | = 9$

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

$6 - 4 x = \pm 9$

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.

$6 - 4 x = 9$

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

Subtract $6$ from both sides of the equation.

$- 4 x = 9 - 6$

Subtract $6$ from $9$ .

$- 4 x = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$6 - 4 x = - 9$

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

Subtract $6$ from both sides of the equation.

$- 4 x = - 9 - 6$

Subtract $6$ from $- 9$ .

$- 4 x = - 15$

Divide each term in $- 4 x = - 15$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 15$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 15}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 15}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{15}{4}$

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

$x = - \frac{3}{4}, \frac{15}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{4}, \frac{15}{4}$

Decimal Form:

$x = - 0.75, 3.75$

Mixed Number Form:

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

Solve the Absolute Value Inequality for x 8+|6-4x|=17

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