Solve for x -8<4(x-2)<=3

$- 8 < 4 (x - 2) \leq 3$

Apply the distributive property.

$- 8 < 4 x + 4 \cdot - 2 \leq 3$

Multiply $4$ by $- 2$ .

$- 8 < 4 x - 8 \leq 3$

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.

$- 8 + 8 < 4 x \leq 3 + 8$

Add $- 8$ and $8$ .

$0 < 4 x \leq 3 + 8$

Add $3$ and $8$ .

$0 < 4 x \leq 11$

Divide each term in the inequality by $4$ .

$\frac{0}{4} < \frac{4 x}{4} \leq \frac{11}{4}$

Divide $0$ by $4$ .

$0 < \frac{4 x}{4} \leq \frac{11}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$0 < \frac{4 x}{4} \leq \frac{11}{4}$

Divide $x$ by $1$ .

$0 < x \leq \frac{11}{4}$

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{11}{4}$

Interval Notation:

$(0, \frac{11}{4}]$