Solve the Inequality for n -6<3n+9<21

$- 6 < 3 n + 9 < 21$

Step 1

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

Subtract $9$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 9 < 3 n < 21 - 9$

Subtract $9$ from $- 6$ .

$- 15 < 3 n < 21 - 9$

Subtract $9$ from $21$ .

$- 15 < 3 n < 12$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 15}{3} < \frac{3 n}{3} < \frac{12}{3}$

Step 3

Divide $- 15$ by $3$ .

$- 5 < \frac{3 n}{3} < \frac{12}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 5 < \frac{3 n}{3} < \frac{12}{3}$

Divide $n$ by $1$ .

$- 5 < n < \frac{12}{3}$

Step 5

Divide $12$ by $3$ .

$- 5 < n < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 < n < 4$

Interval Notation:

$(- 5, 4)$

Step 7