Solve for x -12<4(x-3)<=5

$- 12 < 4 (x - 3) \leq 5$

Apply the distributive property.

$- 12 < 4 x + 4 \cdot - 3 \leq 5$

Multiply $4$ by $- 3$ .

$- 12 < 4 x - 12 \leq 5$

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

Add $12$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 + 12 < 4 x \leq 5 + 12$

Add $- 12$ and $12$ .

$0 < 4 x \leq 5 + 12$

Add $5$ and $12$ .

$0 < 4 x \leq 17$

Divide each term in the inequality by $4$ .

$\frac{0}{4} < \frac{4 x}{4} \leq \frac{17}{4}$

Divide $0$ by $4$ .

$0 < \frac{4 x}{4} \leq \frac{17}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$0 < \frac{4 x}{4} \leq \frac{17}{4}$

Divide $x$ by $1$ .

$0 < x \leq \frac{17}{4}$

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{17}{4}$

Interval Notation:

$(0, \frac{17}{4}]$