Solve for x 2<2x+2<=8

$2 < 2 x + 2 \leq 8$

Step 1

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

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

Subtract $2$ from $2$ .

$0 < 2 x \leq 8 - 2$

Subtract $2$ from $8$ .

$0 < 2 x \leq 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{0}{2} < \frac{2 x}{2} \leq \frac{6}{2}$

Step 3

Divide $0$ by $2$ .

$0 < \frac{2 x}{2} \leq \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$0 < \frac{2 x}{2} \leq \frac{6}{2}$

Divide $x$ by $1$ .

$0 < x \leq \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$0 < x \leq 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq 3$

Interval Notation:

$(0, 3]$

Step 7