Solve for x -7<2x+1<=9

$- 7 < 2 x + 1 \leq 9$

Step 1

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

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

$- 7 - 1 < 2 x \leq 9 - 1$

Subtract $1$ from $- 7$ .

$- 8 < 2 x \leq 9 - 1$

Subtract $1$ from $9$ .

$- 8 < 2 x \leq 8$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 8$ by $2$ .

$- 4 < \frac{2 x}{2} \leq \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 < \frac{2 x}{2} \leq \frac{8}{2}$

Divide $x$ by $1$ .

$- 4 < x \leq \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

$- 4 < x \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x \leq 4$

Interval Notation:

$(- 4, 4]$

Step 7