Solve for x -8<2(x-4)<=5

$- 8 < 2 (x - 4) \leq 5$

Apply the distributive property.

$- 8 < 2 x + 2 \cdot - 4 \leq 5$

Multiply $2$ by $- 4$ .

$- 8 < 2 x - 8 \leq 5$

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

Add $8$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 8 + 8 < 2 x \leq 5 + 8$

Add $- 8$ and $8$ .

$0 < 2 x \leq 5 + 8$

Add $5$ and $8$ .

$0 < 2 x \leq 13$

Divide each term in the inequality by $2$ .

$\frac{0}{2} < \frac{2 x}{2} \leq \frac{13}{2}$

Divide $0$ by $2$ .

$0 < \frac{2 x}{2} \leq \frac{13}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$0 < \frac{2 x}{2} \leq \frac{13}{2}$

Divide $x$ by $1$ .

$0 < x \leq \frac{13}{2}$

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{13}{2}$

Interval Notation:

$(0, \frac{13}{2}]$