Solve for x 12<=-3-5x<=22

$12 \leq - 3 - 5 x \leq 22$

Step 1

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

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$12 + 3 \leq - 5 x \leq 22 + 3$

Add $12$ and $3$ .

$15 \leq - 5 x \leq 22 + 3$

Add $22$ and $3$ .

$15 \leq - 5 x \leq 25$

Step 2

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

$\frac{15}{- 5} \geq \frac{- 5 x}{- 5} \geq \frac{25}{- 5}$

Step 3

Divide $15$ by $- 5$ .

$- 3 \geq \frac{- 5 x}{- 5} \geq \frac{25}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

Cancel the common factor.

$- 3 \geq \frac{- 5 x}{- 5} \geq \frac{25}{- 5}$

Divide $x$ by $1$ .

$- 3 \geq x \geq \frac{25}{- 5}$

Step 5

Divide $25$ by $- 5$ .

$- 3 \geq x \geq - 5$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 5 \leq x \leq - 3$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x \leq - 3$

Interval Notation:

$[- 5, - 3]$

Step 8