Solve for x -10<5(x-2)<=9

$- 10 < 5 (x - 2) \leq 9$

Step 1

Apply the distributive property.

$- 10 < 5 x + 5 \cdot - 2 \leq 9$

Step 2

Multiply $5$ by $- 2$ .

$- 10 < 5 x - 10 \leq 9$

Step 3

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

Add $10$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 10 + 10 < 5 x \leq 9 + 10$

Add $- 10$ and $10$ .

$0 < 5 x \leq 9 + 10$

Add $9$ and $10$ .

$0 < 5 x \leq 19$

Step 4

Divide each term in the inequality by $5$ .

$\frac{0}{5} < \frac{5 x}{5} \leq \frac{19}{5}$

Step 5

Divide $0$ by $5$ .

$0 < \frac{5 x}{5} \leq \frac{19}{5}$

Step 6

Cancel the common factor of $5$ .

Cancel the common factor.

$0 < \frac{5 x}{5} \leq \frac{19}{5}$

Divide $x$ by $1$ .

$0 < x \leq \frac{19}{5}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq \frac{19}{5}$

Interval Notation:

$(0, \frac{19}{5}]$

Step 8