Solve the Inequality for x 4<=-3x-1<=9

$4 \leq - 3 x - 1 \leq 9$

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$4 + 1 \leq - 3 x \leq 9 + 1$

Add $4$ and $1$ .

$5 \leq - 3 x \leq 9 + 1$

Add $9$ and $1$ .

$5 \leq - 3 x \leq 10$

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

$\frac{5}{- 3} \geq \frac{- 3 x}{- 3} \geq \frac{10}{- 3}$

Move the negative in front of the fraction.

$- \frac{5}{3} \geq \frac{- 3 x}{- 3} \geq \frac{10}{- 3}$

Cancel the common factor of $- 3$ .

Cancel the common factor.

$- \frac{5}{3} \geq \frac{- 3 x}{- 3} \geq \frac{10}{- 3}$

Divide $x$ by $1$ .

$- \frac{5}{3} \geq x \geq \frac{10}{- 3}$

Move the negative in front of the fraction.

$- \frac{5}{3} \geq x \geq - \frac{10}{3}$

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

$- \frac{10}{3} \leq x \leq - \frac{5}{3}$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{10}{3} \leq x \leq - \frac{5}{3}$

Interval Notation:

$[- \frac{10}{3}, - \frac{5}{3}]$