Solve for x -32<=3x-5<13

$- 32 \leq 3 x - 5 < 13$

Step 1

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 32 + 5 \leq 3 x < 13 + 5$

Add $- 32$ and $5$ .

$- 27 \leq 3 x < 13 + 5$

Add $13$ and $5$ .

$- 27 \leq 3 x < 18$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 27}{3} \leq \frac{3 x}{3} < \frac{18}{3}$

Step 3

Divide $- 27$ by $3$ .

$- 9 \leq \frac{3 x}{3} < \frac{18}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 9 \leq \frac{3 x}{3} < \frac{18}{3}$

Divide $x$ by $1$ .

$- 9 \leq x < \frac{18}{3}$

Step 5

Divide $18$ by $3$ .

$- 9 \leq x < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 9 \leq x < 6$

Interval Notation:

$[- 9, 6)$

Step 7