Precalculus Examples

$3 = 3 + | 2 x |$

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

$3 + | 2 x | = 3$

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

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Subtract $3$ from both sides of the equation.

$| 2 x | = 3 - 3$

Subtract $3$ from $3$ .

$| 2 x | = 0$

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

$2 x = \pm (0)$

Set up the positive portion of the $\pm$ solution.

$2 x = 0$

Divide each term by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $0$ by $2$ .

$x = 0$

Set up the negative portion of the $\pm$ solution.

$2 x = 0$

Divide each term by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $0$ by $2$ .

$x = 0$

The solution to the equation includes both the positive and negative portions of the solution.

$x = 0$

Verify each of the solutions by substituting them into $3 = 3 + | 2 x |$ and solving.

$x = 0$

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