Pre-Algebra Examples

$2 | x | = 4$

Step 1

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

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Step 1.1

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

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

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

Step 1.2.1.2

Divide $| x |$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $4$ by $2$ .

$| x | = 2$

Step 2

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

$x = \pm 2$

Step 3

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

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 2$

Step 3.2

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

$x = - 2$

Step 3.3

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

$x = 2, - 2$