Solve for x 2|x|=3

$2 | x | = 3$

Step 1

Divide each term in $2 | x | = 3$ by $2$ and simplify.

Divide each term in $2 | x | = 3$ by $2$ .

$\frac{2 | x |}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | x |}{2} = \frac{3}{2}$

Divide $| x |$ by $1$ .

$| x | = \frac{3}{2}$

Step 2

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

$x = \pm \frac{3}{2}$

Step 3

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.

$x = \frac{3}{2}$

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

$x = - \frac{3}{2}$

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5, - 1.5$

Mixed Number Form:

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