Solve for x 2|25x|=100

$2 | 25 x | = 100$

Step 1

Divide each term in $2 | 25 x | = 100$ by $2$ and simplify.

Divide each term in $2 | 25 x | = 100$ by $2$ .

$\frac{2 | 25 x |}{2} = \frac{100}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | 25 x |}{2} = \frac{100}{2}$

Divide $| 25 x |$ by $1$ .

$| 25 x | = \frac{100}{2}$

Remove non-negative terms from the absolute value.

$25 | x | = \frac{100}{2}$

Simplify the right side.

Divide $100$ by $2$ .

$25 | x | = 50$

Step 2

Divide each term in $25 | x | = 50$ by $25$ and simplify.

Divide each term in $25 | x | = 50$ by $25$ .

$\frac{25 | x |}{25} = \frac{50}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 | x |}{25} = \frac{50}{25}$

Divide $| x |$ by $1$ .

$| x | = \frac{50}{25}$

Simplify the right side.

Divide $50$ by $25$ .

$| x | = 2$

Step 3

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

$x = \pm 2$

Step 4

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$