Solve for x -8<-4x<=12

$- 8 < - 4 x \leq 12$

Step 1

Divide each term in the inequality by $- 4$ .

$\frac{- 8}{- 4} > \frac{- 4 x}{- 4} \geq \frac{12}{- 4}$

Step 2

Divide $- 8$ by $- 4$ .

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

Step 3

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

Divide $12$ by $- 4$ .

$2 > x \geq - 3$

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.

$- 3 \leq x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < 2$

Interval Notation:

$[- 3, 2)$

Step 7