Solve the Inequality for x 5<2-3x<8

$5 < 2 - 3 x < 8$

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.

$5 - 2 < - 3 x < 8 - 2$

Subtract $2$ from $5$ .

$3 < - 3 x < 8 - 2$

Subtract $2$ from $8$ .

$3 < - 3 x < 6$

Step 2

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

$\frac{3}{- 3} > \frac{- 3 x}{- 3} > \frac{6}{- 3}$

Step 3

Divide $3$ by $- 3$ .

$- 1 > \frac{- 3 x}{- 3} > \frac{6}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$- 1 > \frac{- 3 x}{- 3} > \frac{6}{- 3}$

Divide $x$ by $1$ .

$- 1 > x > \frac{6}{- 3}$

Step 5

Divide $6$ by $- 3$ .

$- 1 > x > - 2$

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.

$- 2 < x < - 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x < - 1$

Interval Notation:

$(- 2, - 1)$

Step 8