Precalculus Examples

$2 = | 3 x |$

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

$| 3 x | = 2$

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

$3 x = \pm 2$

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

$3 x = 2$

Divide each term by $3$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

$3 x = - 2$

Divide each term by $3$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Move the negative in front of the fraction.

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}, - 0.\overline{6}$

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