Solve the Absolute Value Inequality for x |2x-3|-4=3

$| 2 x - 3 | - 4 = 3$

Move all terms not containing $| 2 x - 3 |$ to the right side of the equation.

Add $4$ to both sides of the equation.

$| 2 x - 3 | = 3 + 4$

Add $3$ and $4$ .

$| 2 x - 3 | = 7$

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

$2 x - 3 = \pm 7$

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.

$2 x - 3 = 7$

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

Add $3$ to both sides of the equation.

$2 x = 7 + 3$

Add $7$ and $3$ .

$2 x = 10$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$

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

$2 x - 3 = - 7$

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

Add $3$ to both sides of the equation.

$2 x = - 7 + 3$

Add $- 7$ and $3$ .

$2 x = - 4$

Divide each term in $2 x = - 4$ by $2$ and simplify.

Divide each term in $2 x = - 4$ by $2$ .

$\frac{2 x}{2} = \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 4}{2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

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

$x = 5, - 2$

Solve the Absolute Value Inequality for x |2x-3|-4=3

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