Precalculus Examples

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

Add $2$ and $3$ .

$2 + | 3 x | = 5$

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

Tap for more steps...

Subtract $2$ from both sides of the equation.

$| 3 x | = - 2 + 5$

Add $- 2$ and $5$ .

$| 3 x | = 3$

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

$3 x = \pm 3$

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

$3 x = 3$

Divide each term by $3$ and simplify.

Tap for more steps...

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

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

Reduce the expression by cancelling the common factors.

Tap for more steps...

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $3$ by $3$ .

$x = 1$

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

$3 x = - 3$

Solve the second equation for $x$ .

Tap for more steps...

Multiply $- 1$ by $3$ .

$3 x = - 3$

Divide each term by $3$ and simplify.

Tap for more steps...

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

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

Reduce the expression by cancelling the common factors.

Tap for more steps...

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side of the equation.

Tap for more steps...

Divide $3$ by $3$ .

$x = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$x = - 1$

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

$x = 1, - 1$

Enter YOUR Problem