Solve for x -13<-3x+2<20

$- 13 < - 3 x + 2 < 20$

Step 1

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 13 - 2 < - 3 x < 20 - 2$

Subtract $2$ from $- 13$ .

$- 15 < - 3 x < 20 - 2$

Subtract $2$ from $20$ .

$- 15 < - 3 x < 18$

Step 2

Divide each term in the inequality by $- 3$ .

$\frac{- 15}{- 3} > \frac{- 3 x}{- 3} > \frac{18}{- 3}$

Step 3

Divide $- 15$ by $- 3$ .

$5 > \frac{- 3 x}{- 3} > \frac{18}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$5 > \frac{- 3 x}{- 3} > \frac{18}{- 3}$

Divide $x$ by $1$ .

$5 > x > \frac{18}{- 3}$

Step 5

Divide $18$ by $- 3$ .

$5 > x > - 6$

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.

$- 6 < x < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x < 5$

Interval Notation:

$(- 6, 5)$

Step 8