Solve the System of Inequalities -16<=-3x-7 or -3x-7<-22

$- 16 \leq - 3 x - 7$ or $- 3 x - 7 < - 22$

Step 1

Simplify the first inequality.

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

$- 3 x - 7 \geq - 16$ or $- 3 x - 7 < - 22$

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

Add $7$ to both sides of the inequality.

$- 3 x \geq - 16 + 7$ or $- 3 x - 7 < - 22$

Add $- 16$ and $7$ .

$- 3 x \geq - 9$ or $- 3 x - 7 < - 22$

Divide each term in $- 3 x \geq - 9$ by $- 3$ and simplify.

Divide each term in $- 3 x \geq - 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \leq \frac{- 9}{- 3}$ or $- 3 x - 7 < - 22$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \leq \frac{- 9}{- 3}$ or $- 3 x - 7 < - 22$

Divide $x$ by $1$ .

$x \leq \frac{- 9}{- 3}$ or $- 3 x - 7 < - 22$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$x \leq 3$ or $- 3 x - 7 < - 22$

Step 2

Simplify the second inequality.

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

Add $7$ to both sides of the inequality.

$x \leq 3$ or $- 3 x < - 22 + 7$

Add $- 22$ and $7$ .

$x \leq 3$ or $- 3 x < - 15$

Divide each term in $- 3 x < - 15$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 15$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \leq 3$ or $\frac{- 3 x}{- 3} > \frac{- 15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x \leq 3$ or $\frac{- 3 x}{- 3} > \frac{- 15}{- 3}$

Divide $x$ by $1$ .

$x \leq 3$ or $x > \frac{- 15}{- 3}$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$x \leq 3$ or $x > 5$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3 or x > 5$

Interval Notation:

$(- \infty, 3] \cup (5, \infty)$

Step 4

Solve the System of Inequalities -16<=-3x-7 or -3x-7<-22

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