Solve for n 2<-2n+20<=4

$2 < - 2 n + 20 \leq 4$

Step 1

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

Subtract $20$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$2 - 20 < - 2 n \leq 4 - 20$

Subtract $20$ from $2$ .

$- 18 < - 2 n \leq 4 - 20$

Subtract $20$ from $4$ .

$- 18 < - 2 n \leq - 16$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{- 18}{- 2} > \frac{- 2 n}{- 2} \geq \frac{- 16}{- 2}$

Step 3

Divide $- 18$ by $- 2$ .

$9 > \frac{- 2 n}{- 2} \geq \frac{- 16}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$9 > \frac{- 2 n}{- 2} \geq \frac{- 16}{- 2}$

Divide $n$ by $1$ .

$9 > n \geq \frac{- 16}{- 2}$

Step 5

Divide $- 16$ by $- 2$ .

$9 > n \geq 8$

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.

$8 \leq n < 9$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$8 \leq n < 9$

Interval Notation:

$[8, 9)$

Step 8