Solve the Inequality for n -33<=-7n-12<-26

$- 33 \leq - 7 n - 12 < - 26$

Step 1

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

Add $12$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 33 + 12 \leq - 7 n < - 26 + 12$

Add $- 33$ and $12$ .

$- 21 \leq - 7 n < - 26 + 12$

Add $- 26$ and $12$ .

$- 21 \leq - 7 n < - 14$

Step 2

Divide each term in the inequality by $- 7$ .

$\frac{- 21}{- 7} \geq \frac{- 7 n}{- 7} > \frac{- 14}{- 7}$

Step 3

Divide $- 21$ by $- 7$ .

$3 \geq \frac{- 7 n}{- 7} > \frac{- 14}{- 7}$

Step 4

Cancel the common factor of $- 7$ .

Cancel the common factor.

$3 \geq \frac{- 7 n}{- 7} > \frac{- 14}{- 7}$

Divide $n$ by $1$ .

$3 \geq n > \frac{- 14}{- 7}$

Step 5

Divide $- 14$ by $- 7$ .

$3 \geq n > 2$

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.

$2 < n \leq 3$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$2 < n \leq 3$

Interval Notation:

$(2, 3]$

Step 8