Solve the Inequality for x 3<=-6-5x<12

$3 \leq - 6 - 5 x < 12$

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

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$3 + 6 \leq - 5 x < 12 + 6$

Add $3$ and $6$ .

$9 \leq - 5 x < 12 + 6$

Add $12$ and $6$ .

$9 \leq - 5 x < 18$

Divide each term in the inequality by $- 5$ .

$\frac{9}{- 5} \geq \frac{- 5 x}{- 5} > \frac{18}{- 5}$

Move the negative in front of the fraction.

$- \frac{9}{5} \geq \frac{- 5 x}{- 5} > \frac{18}{- 5}$

Cancel the common factor of $- 5$ .

Cancel the common factor.

$- \frac{9}{5} \geq \frac{- 5 x}{- 5} > \frac{18}{- 5}$

Divide $x$ by $1$ .

$- \frac{9}{5} \geq x > \frac{18}{- 5}$

Move the negative in front of the fraction.

$- \frac{9}{5} \geq x > - \frac{18}{5}$

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

$- \frac{18}{5} < x \leq - \frac{9}{5}$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{18}{5} < x \leq - \frac{9}{5}$

Interval Notation:

$(- \frac{18}{5}, - \frac{9}{5}]$