Solve the System of Inequalities -6<=2x+6<=6

$- 6 \leq 2 x + 6 \leq 6$

Step 1

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

Rewrite so $x$ is on the left side of the inequality.

$2 x + 6 \geq - 6$

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

Subtract $6$ from both sides of the inequality.

$2 x \geq - 6 - 6$

Subtract $6$ from $- 6$ .

$2 x \geq - 12$

Divide each term in $2 x \geq - 12$ by $2$ and simplify.

Divide each term in $2 x \geq - 12$ by $2$ .

$\frac{2 x}{2} \geq \frac{- 12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{- 12}{2}$

Divide $x$ by $1$ .

$x \geq \frac{- 12}{2}$

Simplify the right side.

Divide $- 12$ by $2$ .

$x \geq - 6$

Step 2

Solve $2 x + 6 \leq 6$ for $x$ .

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

Subtract $6$ from both sides of the inequality.

$2 x \leq 6 - 6$

Subtract $6$ from $6$ .

$2 x \leq 0$

Divide each term in $2 x \leq 0$ by $2$ and simplify.

Divide each term in $2 x \leq 0$ by $2$ .

$\frac{2 x}{2} \leq \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{0}{2}$

Divide $x$ by $1$ .

$x \leq \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x \leq 0$

Step 3

Find the intersection of $x \geq - 6$ and $x \leq 0$ .

$- 6 \leq x \leq 0$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq x \leq 0$

Interval Notation:

$[- 6, 0]$

Step 5

Solve the System of Inequalities -6<=2x+6<=6

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