Solve the Inequality for x -12<=2x-2<-4

$- 12 \leq 2 x - 2 < - 4$

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.

$- 12 + 2 \leq 2 x < - 4 + 2$

Add $- 12$ and $2$ .

$- 10 \leq 2 x < - 4 + 2$

Add $- 4$ and $2$ .

$- 10 \leq 2 x < - 2$

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} \leq \frac{2 x}{2} < \frac{- 2}{2}$

Divide $- 10$ by $2$ .

$- 5 \leq \frac{2 x}{2} < \frac{- 2}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 \leq \frac{2 x}{2} < \frac{- 2}{2}$

Divide $x$ by $1$ .

$- 5 \leq x < \frac{- 2}{2}$

Divide $- 2$ by $2$ .

$- 5 \leq x < - 1$

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x < - 1$

Interval Notation:

$[- 5, - 1)$