Solve for x 3<2x+1<=9

$3 < 2 x + 1 \leq 9$

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.

$3 - 1 < 2 x \leq 9 - 1$

Subtract $1$ from $3$ .

$2 < 2 x \leq 9 - 1$

Subtract $1$ from $9$ .

$2 < 2 x \leq 8$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $2$ by $2$ .

$1 < \frac{2 x}{2} \leq \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$1 < \frac{2 x}{2} \leq \frac{8}{2}$

Divide $x$ by $1$ .

$1 < x \leq \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

$1 < x \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 < x \leq 4$

Interval Notation:

$(1, 4]$

Step 7