Solve for x -13<4x-1<=-9

$- 13 < 4 x - 1 \leq - 9$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 13 + 1 < 4 x \leq - 9 + 1$

Add $- 13$ and $1$ .

$- 12 < 4 x \leq - 9 + 1$

Add $- 9$ and $1$ .

$- 12 < 4 x \leq - 8$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 12}{4} < \frac{4 x}{4} \leq \frac{- 8}{4}$

Step 3

Divide $- 12$ by $4$ .

$- 3 < \frac{4 x}{4} \leq \frac{- 8}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$- 3 < \frac{4 x}{4} \leq \frac{- 8}{4}$

Divide $x$ by $1$ .

$- 3 < x \leq \frac{- 8}{4}$

Step 5

Divide $- 8$ by $4$ .

$- 3 < x \leq - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x \leq - 2$

Interval Notation:

$(- 3, - 2]$

Step 7