Solve for x 2<2x-4<=8

$2 < 2 x - 4 \leq 8$

Step 1

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$2 + 4 < 2 x \leq 8 + 4$

Add $2$ and $4$ .

$6 < 2 x \leq 8 + 4$

Add $8$ and $4$ .

$6 < 2 x \leq 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{6}{2} < \frac{2 x}{2} \leq \frac{12}{2}$

Step 3

Divide $6$ by $2$ .

$3 < \frac{2 x}{2} \leq \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3 < \frac{2 x}{2} \leq \frac{12}{2}$

Divide $x$ by $1$ .

$3 < x \leq \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$3 < x \leq 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$3 < x \leq 6$

Interval Notation:

$(3, 6]$

Step 7