Find All Complex Solutions |2x-3|=9

$| 2 x - 3 | = 9$

Step 1

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

$2 x - 3 = \pm 9$

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.

$2 x - 3 = 9$

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

Add $3$ to both sides of the equation.

$2 x = 9 + 3$

Add $9$ 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 $2$ .

$x = 6$

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

$2 x - 3 = - 9$

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

Add $3$ to both sides of the equation.

$2 x = - 9 + 3$

Add $- 9$ and $3$ .

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

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

$x = 6, - 3$

Find All Complex Solutions |2x-3|=9

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