Algebra Examples Absolute Value Expressions and Equations

Solve for x

$3 = 3 + | 2 x |$

Step 1

Rewrite the equation as $3 + | 2 x | = 3$ .

$3 + | 2 x | = 3$

Step 2

Move all terms not containing $| 2 x |$ to the right side of the equation.

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Step 2.1

Subtract $3$ from both sides of the equation.

$| 2 x | = 3 - 3$

Step 2.2

Subtract $3$ from $3$ .

$| 2 x | = 0$

Step 3

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

$2 x = \pm 0$

Step 4

Plus or minus $0$ is $0$ .

$2 x = 0$

Step 5

Divide each term in $2 x = 0$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $2$ .

$x = 0$

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Absolute Value Expressions and Equations

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