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

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

Step 1

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

Add $12$ to each section of the inequality because it does not contain the variable we are trying to solve for.

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

Add $- 4$ and $12$ .

$8 \leq - 4 x < 4 + 12$

Add $4$ and $12$ .

$8 \leq - 4 x < 16$

Step 2

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

$\frac{8}{- 4} \geq \frac{- 4 x}{- 4} > \frac{16}{- 4}$

Step 3

Divide $8$ by $- 4$ .

$- 2 \geq \frac{- 4 x}{- 4} > \frac{16}{- 4}$

Step 4

Cancel the common factor of $- 4$ .

Cancel the common factor.

$- 2 \geq \frac{- 4 x}{- 4} > \frac{16}{- 4}$

Divide $x$ by $1$ .

$- 2 \geq x > \frac{16}{- 4}$

Step 5

Divide $16$ by $- 4$ .

$- 2 \geq x > - 4$

Step 6

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

$- 4 < x \leq - 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x \leq - 2$

Interval Notation:

$(- 4, - 2]$

Step 8