Solve for n -6<2n+4<18

$- 6 < 2 n + 4 < 18$

Step 1

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

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 4 < 2 n < 18 - 4$

Subtract $4$ from $- 6$ .

$- 10 < 2 n < 18 - 4$

Subtract $4$ from $18$ .

$- 10 < 2 n < 14$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 n}{2} < \frac{14}{2}$

Step 3

Divide $- 10$ by $2$ .

$- 5 < \frac{2 n}{2} < \frac{14}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 < \frac{2 n}{2} < \frac{14}{2}$

Divide $n$ by $1$ .

$- 5 < n < \frac{14}{2}$

Step 5

Divide $14$ by $2$ .

$- 5 < n < 7$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 < n < 7$

Interval Notation:

$(- 5, 7)$

Step 7