Precalculus Examples

$3 + | 2 x | = 3 + 3$

Add $3$ and $3$ .

$3 + | 2 x | = 6$

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.

$| 2 x | = 6 - 3$

Subtract $3$ from $6$ .

$| 2 x | = 3$

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

$2 x = \pm 3$

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

$2 x = 3$

Divide each term by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

$2 x = - 3$

Divide each term by $2$ and simplify.

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Move the negative in front of the fraction.

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

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

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

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:

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

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