Solve for x -15<3(x-5)<=1

$- 15 < 3 (x - 5) \leq 1$

Step 1

Apply the distributive property.

$- 15 < 3 x + 3 \cdot - 5 \leq 1$

Step 2

Multiply $3$ by $- 5$ .

$- 15 < 3 x - 15 \leq 1$

Step 3

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

Add $15$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 15 + 15 < 3 x \leq 1 + 15$

Add $- 15$ and $15$ .

$0 < 3 x \leq 1 + 15$

Add $1$ and $15$ .

$0 < 3 x \leq 16$

Step 4

Divide each term in the inequality by $3$ .

$\frac{0}{3} < \frac{3 x}{3} \leq \frac{16}{3}$

Step 5

Divide $0$ by $3$ .

$0 < \frac{3 x}{3} \leq \frac{16}{3}$

Step 6

Cancel the common factor of $3$ .

Cancel the common factor.

$0 < \frac{3 x}{3} \leq \frac{16}{3}$

Divide $x$ by $1$ .

$0 < x \leq \frac{16}{3}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{16}{3}$

Interval Notation:

$(0, \frac{16}{3}]$

Step 8