Solve for x -6<-4x-6<46

$- 6 < - 4 x - 6 < 46$

Step 1

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

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 + 6 < - 4 x < 46 + 6$

Add $- 6$ and $6$ .

$0 < - 4 x < 46 + 6$

Add $46$ and $6$ .

$0 < - 4 x < 52$

Step 2

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

$\frac{0}{- 4} > \frac{- 4 x}{- 4} > \frac{52}{- 4}$

Step 3

Divide $0$ by $- 4$ .

$0 > \frac{- 4 x}{- 4} > \frac{52}{- 4}$

Step 4

Cancel the common factor of $- 4$ .

Cancel the common factor.

$0 > \frac{- 4 x}{- 4} > \frac{52}{- 4}$

Divide $x$ by $1$ .

$0 > x > \frac{52}{- 4}$

Step 5

Divide $52$ by $- 4$ .

$0 > x > - 13$

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.

$- 13 < x < 0$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 13 < x < 0$

Interval Notation:

$(- 13, 0)$

Step 8