Convert to Interval Notation -12<12+4x<0

$- 12 < 12 + 4 x < 0$

Step 1

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

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

$- 12 - 12 < 4 x < 0 - 12$

Subtract $12$ from $- 12$ .

$- 24 < 4 x < 0 - 12$

Subtract $12$ from $0$ .

$- 24 < 4 x < - 12$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 24}{4} < \frac{4 x}{4} < \frac{- 12}{4}$

Step 3

Divide $- 24$ by $4$ .

$- 6 < \frac{4 x}{4} < \frac{- 12}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$- 6 < \frac{4 x}{4} < \frac{- 12}{4}$

Divide $x$ by $1$ .

$- 6 < x < \frac{- 12}{4}$

Step 5

Divide $- 12$ by $4$ .

$- 6 < x < - 3$

Step 6

Convert the inequality to interval notation.

$(- 6, - 3)$

Step 7