Graph |3x|<=12

$| 3 x | \leq 12$

Step 1

Write $| 3 x | \leq 12$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$3 x \geq 0$

Divide each term in $3 x \geq 0$ by $3$ and simplify.

Divide each term in $3 x \geq 0$ by $3$ .

$\frac{3 x}{3} \geq \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{0}{3}$

Divide $x$ by $1$ .

$x \geq \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x \geq 0$

In the piece where $3 x$ is non-negative, remove the absolute value.

$3 x \leq 12$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$3 x < 0$

Divide each term in $3 x < 0$ by $3$ and simplify.

Divide each term in $3 x < 0$ by $3$ .

$\frac{3 x}{3} < \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{0}{3}$

Divide $x$ by $1$ .

$x < \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x < 0$

In the piece where $3 x$ is negative, remove the absolute value and multiply by $- 1$ .

$- 3 x \leq 12$

Write as a piecewise.

${\begin{cases} 3 x \leq 12 & x \geq 0 \\ - 3 x \leq 12 & x < 0 \end{cases}$

Step 2

Solve $3 x \leq 12$ when $x \geq 0$ .

Divide each term in $3 x \leq 12$ by $3$ and simplify.

Divide each term in $3 x \leq 12$ by $3$ .

$\frac{3 x}{3} \leq \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{12}{3}$

Divide $x$ by $1$ .

$x \leq \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x \leq 4$

Find the intersection of $x \leq 4$ and $x \geq 0$ .

$0 \leq x \leq 4$

Step 3

Solve $- 3 x \leq 12$ when $x < 0$ .

Divide each term in $- 3 x \leq 12$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{12}{- 3}$

Divide $x$ by $1$ .

$x \geq \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$x \geq - 4$

Find the intersection of $x \geq - 4$ and $x < 0$ .

$- 4 \leq x < 0$

Step 4

Find the union of the solutions.

$- 4 \leq x \leq 4$

Step 5

Graph |3x|<=12

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