Solve the System of Inequalities -22>-5x-7>=-3

$- 22 > - 5 x - 7 \geq - 3$

Solve $- 22 > - 5 x - 7$ for $x$ .

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

$- 5 x - 7 < - 22$

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

Add $7$ to both sides of the inequality.

$- 5 x < - 22 + 7$

Add $- 22$ and $7$ .

$- 5 x < - 15$

Divide each term in $- 5 x < - 15$ by $- 5$ and simplify.

Divide each term in $- 5 x < - 15$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} > \frac{- 15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} > \frac{- 15}{- 5}$

Divide $x$ by $1$ .

$x > \frac{- 15}{- 5}$

Simplify the right side.

Divide $- 15$ by $- 5$ .

$x > 3$

Solve $- 5 x - 7 \geq - 3$ for $x$ .

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

Add $7$ to both sides of the inequality.

$- 5 x \geq - 3 + 7$

Add $- 3$ and $7$ .

$- 5 x \geq 4$

Divide each term in $- 5 x \geq 4$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq 4$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{4}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{4}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{4}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x \leq - \frac{4}{5}$

Find the intersection of $x > 3$ and $x \leq - \frac{4}{5}$ .

No solution

Solve the System of Inequalities -22>-5x-7>=-3

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