Graph 2|x|-6<=10

$2 | x | - 6 \leq 10$

Step 1

Write $2 | x | - 6 \leq 10$ as a piecewise.

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

$x \geq 0$

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

$2 x - 6 \leq 10$

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

$x < 0$

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

$2 (- x) - 6 \leq 10$

Write as a piecewise.

${\begin{cases} 2 x - 6 \leq 10 & x \geq 0 \\ 2 (- x) - 6 \leq 10 & x < 0 \end{cases}$

Multiply $- 1$ by $2$ .

${\begin{cases} 2 x - 6 \leq 10 & x \geq 0 \\ - 2 x - 6 \leq 10 & x < 0 \end{cases}$

Step 2

Solve $2 x - 6 \leq 10$ when $x \geq 0$ .

Solve $2 x - 6 \leq 10$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $6$ to both sides of the inequality.

$2 x \leq 10 + 6$

Add $10$ and $6$ .

$2 x \leq 16$

Divide each term in $2 x \leq 16$ by $2$ and simplify.

Divide each term in $2 x \leq 16$ by $2$ .

$\frac{2 x}{2} \leq \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{16}{2}$

Divide $x$ by $1$ .

$x \leq \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$x \leq 8$

Find the intersection of $x \leq 8$ and $x \geq 0$ .

$0 \leq x \leq 8$

Step 3

Solve $- 2 x - 6 \leq 10$ when $x < 0$ .

Solve $- 2 x - 6 \leq 10$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $6$ to both sides of the inequality.

$- 2 x \leq 10 + 6$

Add $10$ and $6$ .

$- 2 x \leq 16$

Divide each term in $- 2 x \leq 16$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq 16$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{16}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{16}{- 2}$

Simplify the right side.

Divide $16$ by $- 2$ .

$x \geq - 8$

Find the intersection of $x \geq - 8$ and $x < 0$ .

$- 8 \leq x < 0$

Step 4

Find the union of the solutions.

$- 8 \leq x \leq 8$

Step 5

Graph 2|x|-6<=10

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