Solve the System of Inequalities 7<=-x-1 or -x-1<=-12

$7 \leq - x - 1$ or $- x - 1 \leq - 12$

Step 1

Simplify the first inequality.

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

$- x - 1 \geq 7$

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

Add $1$ to both sides of the inequality.

$- x \geq 7 + 1$

Add $7$ and $1$ .

$- x \geq 8$

Divide each term in $- x \geq 8$ by $- 1$ and simplify.

Divide each term in $- x \geq 8$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{8}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{8}{- 1}$

Simplify the right side.

Divide $8$ by $- 1$ .

$x \leq - 8$

Step 2

Simplify the second inequality.

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

Add $1$ to both sides of the inequality.

$- x \leq - 12 + 1$

Add $- 12$ and $1$ .

$- x \leq - 11$

Divide each term in $- x \leq - 11$ by $- 1$ and simplify.

Divide each term in $- x \leq - 11$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 11}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{- 11}{- 1}$

Simplify the right side.

Divide $- 11$ by $- 1$ .

$x \geq 11$

Step 3

The union consists of all of the elements that are contained in each interval.

$x \leq - 8$ or $x \geq 11$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 8 or x \geq 11$

Interval Notation:

$(- \infty, - 8] \cup [11, \infty)$

Step 5

Solve the System of Inequalities 7<=-x-1 or -x-1<=-12

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