Solve for x -50<20x-10<=50

$- 50 < 20 x - 10 \leq 50$

Step 1

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.

$- 50 + 10 < 20 x \leq 50 + 10$

Add $- 50$ and $10$ .

$- 40 < 20 x \leq 50 + 10$

Add $50$ and $10$ .

$- 40 < 20 x \leq 60$

Step 2

Divide each term in the inequality by $20$ .

$\frac{- 40}{20} < \frac{20 x}{20} \leq \frac{60}{20}$

Step 3

Divide $- 40$ by $20$ .

$- 2 < \frac{20 x}{20} \leq \frac{60}{20}$

Step 4

Cancel the common factor of $20$ .

Cancel the common factor.

$- 2 < \frac{20 x}{20} \leq \frac{60}{20}$

Divide $x$ by $1$ .

$- 2 < x \leq \frac{60}{20}$

Step 5

Divide $60$ by $20$ .

$- 2 < x \leq 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < x \leq 3$

Interval Notation:

$(- 2, 3]$

Step 7