Solve for x -9<2x-1<=1

$- 9 < 2 x - 1 \leq 1$

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.

$- 9 + 1 < 2 x \leq 1 + 1$

Add $- 9$ and $1$ .

$- 8 < 2 x \leq 1 + 1$

Add $1$ and $1$ .

$- 8 < 2 x \leq 2$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 8}{2} < \frac{2 x}{2} \leq \frac{2}{2}$

Step 3

Divide $- 8$ by $2$ .

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $2$ by $2$ .

$- 4 < x \leq 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x \leq 1$

Interval Notation:

$(- 4, 1]$

Step 7