Solve the Absolute Value Inequality for x |4x-3|=17

$| 4 x - 3 | = 17$

Step 1

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

$4 x - 3 = \pm 17$

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.

$4 x - 3 = 17$

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

Add $3$ to both sides of the equation.

$4 x = 17 + 3$

Add $17$ and $3$ .

$4 x = 20$

Divide each term in $4 x = 20$ by $4$ and simplify.

Divide each term in $4 x = 20$ by $4$ .

$\frac{4 x}{4} = \frac{20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{20}{4}$

Divide $x$ by $1$ .

$x = \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

$x = 5$

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

$4 x - 3 = - 17$

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

Add $3$ to both sides of the equation.

$4 x = - 17 + 3$

Add $- 17$ and $3$ .

$4 x = - 14$

Divide each term in $4 x = - 14$ by $4$ and simplify.

Divide each term in $4 x = - 14$ by $4$ .

$\frac{4 x}{4} = \frac{- 14}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 14}{4}$

Divide $x$ by $1$ .

$x = \frac{- 14}{4}$

Simplify the right side.

Cancel the common factor of $- 14$ and $4$ .

Factor $2$ out of $- 14$ .

$x = \frac{2 (- 7)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 7}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 7}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 7}{2}$

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

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

$x = 5, - \frac{7}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 5, - \frac{7}{2}$

Decimal Form:

$x = 5, - 3.5$

Mixed Number Form:

$x = 5, - 3 \frac{1}{2}$

Solve the Absolute Value Inequality for x |4x-3|=17

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