Solve the Inequality for x -50<-5x-5<-25

$- 50 < - 5 x - 5 < - 25$

Step 1

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 50 + 5 < - 5 x < - 25 + 5$

Add $- 50$ and $5$ .

$- 45 < - 5 x < - 25 + 5$

Add $- 25$ and $5$ .

$- 45 < - 5 x < - 20$

Step 2

Divide each term in the inequality by $- 5$ .

$\frac{- 45}{- 5} > \frac{- 5 x}{- 5} > \frac{- 20}{- 5}$

Step 3

Divide $- 45$ by $- 5$ .

$9 > \frac{- 5 x}{- 5} > \frac{- 20}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

Cancel the common factor.

$9 > \frac{- 5 x}{- 5} > \frac{- 20}{- 5}$

Divide $x$ by $1$ .

$9 > x > \frac{- 20}{- 5}$

Step 5

Divide $- 20$ by $- 5$ .

$9 > x > 4$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$4 < x < 9$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$4 < x < 9$

Interval Notation:

$(4, 9)$

Step 8