Solve for x -7<=-2x-6<-3

$- 7 \leq - 2 x - 6 < - 3$

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.

$- 7 + 6 \leq - 2 x < - 3 + 6$

Add $- 7$ and $6$ .

$- 1 \leq - 2 x < - 3 + 6$

Add $- 3$ and $6$ .

$- 1 \leq - 2 x < 3$

Divide each term in the inequality by $- 2$ .

$\frac{- 1}{- 2} \geq \frac{- 2 x}{- 2} > \frac{3}{- 2}$

Dividing two negative values results in a positive value.

$\frac{1}{2} \geq \frac{- 2 x}{- 2} > \frac{3}{- 2}$

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{1}{2} \geq \frac{- 2 x}{- 2} > \frac{3}{- 2}$

Divide $x$ by $1$ .

$\frac{1}{2} \geq x > \frac{3}{- 2}$

Move the negative in front of the fraction.

$\frac{1}{2} \geq x > - \frac{3}{2}$

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

$- \frac{3}{2} < x \leq \frac{1}{2}$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} < x \leq \frac{1}{2}$

Interval Notation:

$(- \frac{3}{2}, \frac{1}{2}]$