Solve for x -8<-2x<=12

$- 8 < - 2 x \leq 12$

Step 1

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

$\frac{- 8}{- 2} > \frac{- 2 x}{- 2} \geq \frac{12}{- 2}$

Step 2

Divide $- 8$ by $- 2$ .

$4 > \frac{- 2 x}{- 2} \geq \frac{12}{- 2}$

Step 3

Cancel the common factor of $- 2$ .

Cancel the common factor.

$4 > \frac{- 2 x}{- 2} \geq \frac{12}{- 2}$

Divide $x$ by $1$ .

$4 > x \geq \frac{12}{- 2}$

Step 4

Divide $12$ by $- 2$ .

$4 > x \geq - 6$

Step 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.

$- 6 \leq x < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq x < 4$

Interval Notation:

$[- 6, 4)$

Step 7