Solve for x -22>-5x-7>=-3

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

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Add $7$ to each section of the inequality because it does not contain the variable we are trying to solve for.

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

Add $- 22$ and $7$ .

$- 15 > - 5 x \geq - 3 + 7$

Add $- 3$ and $7$ .

$- 15 > - 5 x \geq 4$

Step 2

Divide each term in the inequality by $- 5$ .

$\frac{- 15}{- 5} < \frac{- 5 x}{- 5} \leq \frac{4}{- 5}$

Step 3

Divide $- 15$ by $- 5$ .

$3 < \frac{- 5 x}{- 5} \leq \frac{4}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

Cancel the common factor.

$3 < \frac{- 5 x}{- 5} \leq \frac{4}{- 5}$

Divide $x$ by $1$ .

$3 < x \leq \frac{4}{- 5}$

Step 5

Move the negative in front of the fraction.

$3 < x \leq - \frac{4}{5}$

Step 6

Since the inequality can never be true, there is no solution.

False