Algebra Examples

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

Add $2$ and $3$ .

$| 3 x | + 3 = 5$

Move all terms not containing $| 3 x |$ to the right side of the equation.

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Subtract $3$ from both sides of the equation.

$| 3 x | = - 3 + 5$

Add $- 3$ and $5$ .

$| 3 x | = 2$

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.

$3 x = - 2$

Solve the second equation for $x$ .

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Multiply $- 1$ by $2$ .

$3 x = - 2$

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 $1$ .

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

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 both exact and decimal forms.

Exact Form:

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

Decimal Form:

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

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