Solve for k -10<-5k-15<25

$- 10 < - 5 k - 15 < 25$

Move all terms not containing $k$ 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.

$- 10 + 15 < - 5 k < 25 + 15$

Add $- 10$ and $15$ .

$5 < - 5 k < 25 + 15$

Add $25$ and $15$ .

$5 < - 5 k < 40$

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

$\frac{5}{- 5} > \frac{- 5 k}{- 5} > \frac{40}{- 5}$

Divide $5$ by $- 5$ .

$- 1 > \frac{- 5 k}{- 5} > \frac{40}{- 5}$

Cancel the common factor of $- 5$ .

Cancel the common factor.

$- 1 > \frac{- 5 k}{- 5} > \frac{40}{- 5}$

Divide $k$ by $1$ .

$- 1 > k > \frac{40}{- 5}$

Divide $40$ by $- 5$ .

$- 1 > k > - 8$

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

$- 8 < k < - 1$

The result can be shown in multiple forms.

Inequality Form:

$- 8 < k < - 1$

Interval Notation:

$(- 8, - 1)$