Solve for x |2x-3|=15

$| 2 x - 3 | = 15$

Step 1

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

$2 x - 3 = \pm 15$

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.

$2 x - 3 = 15$

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

Add $3$ to both sides of the equation.

$2 x = 15 + 3$

Add $15$ and $3$ .

$2 x = 18$

Divide each term in $2 x = 18$ by $2$ and simplify.

Divide each term in $2 x = 18$ by $2$ .

$\frac{2 x}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{18}{2}$

Divide $x$ by $1$ .

$x = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$x = 9$

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

$2 x - 3 = - 15$

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

Add $3$ to both sides of the equation.

$2 x = - 15 + 3$

Add $- 15$ and $3$ .

$2 x = - 12$

Divide each term in $2 x = - 12$ by $2$ and simplify.

Divide each term in $2 x = - 12$ by $2$ .

$\frac{2 x}{2} = \frac{- 12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 12}{2}$

Divide $x$ by $1$ .

$x = \frac{- 12}{2}$

Simplify the right side.

Divide $- 12$ by $2$ .

$x = - 6$

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

$x = 9, - 6$

Solve for x |2x-3|=15

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