Solve the System of Inequalities -20<=-x-10<=-16

$- 20 \leq - x - 10 \leq - 16$

Solve $- 20 \leq - x - 10$ for $x$ .

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

$- x - 10 \geq - 20$

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

Add $10$ to both sides of the inequality.

$- x \geq - 20 + 10$

Add $- 20$ and $10$ .

$- x \geq - 10$

Divide each term in $- x \geq - 10$ by $- 1$ and simplify.

Divide each term in $- x \geq - 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- 10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- 10}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{- 10}{- 1}$

Simplify the right side.

Divide $- 10$ by $- 1$ .

$x \leq 10$

Solve $- x - 10 \leq - 16$ for $x$ .

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

Add $10$ to both sides of the inequality.

$- x \leq - 16 + 10$

Add $- 16$ and $10$ .

$- x \leq - 6$

Divide each term in $- x \leq - 6$ by $- 1$ and simplify.

Divide each term in $- x \leq - 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x \geq 6$

Find the intersection of $x \leq 10$ and $x \geq 6$ .

$6 \leq x \leq 10$

The result can be shown in multiple forms.

Inequality Form:

$6 \leq x \leq 10$

Interval Notation:

$[6, 10]$

Solve the System of Inequalities -20<=-x-10<=-16

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