Solve for x -11<2x-1<=-5

$- 11 < 2 x - 1 \leq - 5$

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.

$- 11 + 1 < 2 x \leq - 5 + 1$

Add $- 11$ and $1$ .

$- 10 < 2 x \leq - 5 + 1$

Add $- 5$ and $1$ .

$- 10 < 2 x \leq - 4$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 x}{2} \leq \frac{- 4}{2}$

Step 3

Divide $- 10$ by $2$ .

$- 5 < \frac{2 x}{2} \leq \frac{- 4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 < \frac{2 x}{2} \leq \frac{- 4}{2}$

Divide $x$ by $1$ .

$- 5 < x \leq \frac{- 4}{2}$

Step 5

Divide $- 4$ by $2$ .

$- 5 < x \leq - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x \leq - 2$

Interval Notation:

$(- 5, - 2]$

Step 7