Solve for x 5<=-3x-2<8

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

Step 1

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

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

$5 + 2 \leq - 3 x < 8 + 2$

Add $5$ and $2$ .

$7 \leq - 3 x < 8 + 2$

Add $8$ and $2$ .

$7 \leq - 3 x < 10$

Step 2

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

$\frac{7}{- 3} \geq \frac{- 3 x}{- 3} > \frac{10}{- 3}$

Step 3

Move the negative in front of the fraction.

$- \frac{7}{3} \geq \frac{- 3 x}{- 3} > \frac{10}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$- \frac{7}{3} \geq \frac{- 3 x}{- 3} > \frac{10}{- 3}$

Divide $x$ by $1$ .

$- \frac{7}{3} \geq x > \frac{10}{- 3}$

Step 5

Move the negative in front of the fraction.

$- \frac{7}{3} \geq x > - \frac{10}{3}$

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.

$- \frac{10}{3} < x \leq - \frac{7}{3}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- \frac{10}{3} < x \leq - \frac{7}{3}$

Interval Notation:

$(- \frac{10}{3}, - \frac{7}{3}]$

Step 8