Solve for x -12<3(x-4)<=1

$- 12 < 3 (x - 4) \leq 1$

Step 1

Apply the distributive property.

$- 12 < 3 x + 3 \cdot - 4 \leq 1$

Step 2

Multiply $3$ by $- 4$ .

$- 12 < 3 x - 12 \leq 1$

Step 3

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.

$- 12 + 12 < 3 x \leq 1 + 12$

Add $- 12$ and $12$ .

$0 < 3 x \leq 1 + 12$

Add $1$ and $12$ .

$0 < 3 x \leq 13$

Step 4

Divide each term in the inequality by $3$ .

$\frac{0}{3} < \frac{3 x}{3} \leq \frac{13}{3}$

Step 5

Divide $0$ by $3$ .

$0 < \frac{3 x}{3} \leq \frac{13}{3}$

Step 6

Cancel the common factor of $3$ .

Cancel the common factor.

$0 < \frac{3 x}{3} \leq \frac{13}{3}$

Divide $x$ by $1$ .

$0 < x \leq \frac{13}{3}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{13}{3}$

Interval Notation:

$(0, \frac{13}{3}]$

Step 8