Solve the Inequality for n 2/3n>-12

$\frac{2}{3} n > - 12$

Step 1

Multiply each term in $\frac{2}{3} n > - 12$ by $\frac{3}{2}$ .

$\frac{2}{3} n \frac{3}{2} > - 12 (\frac{3}{2})$

Step 2

Simplify the left side.

Combine $\frac{2}{3}$ and $n$ .

$\frac{2 n}{3} \cdot \frac{3}{2} > - 12 (\frac{3}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $2 n$ .

$\frac{2 (n)}{3} \cdot \frac{3}{2} > - 12 (\frac{3}{2})$

Cancel the common factor.

$\frac{2 n}{3} \cdot \frac{3}{2} > - 12 (\frac{3}{2})$

Rewrite the expression.

$\frac{n}{3} \cdot 3 > - 12 (\frac{3}{2})$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{n}{3} \cdot 3 > - 12 (\frac{3}{2})$

Rewrite the expression.

$n > - 12 (\frac{3}{2})$

Step 3

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $- 12$ .

$n > 2 (- 6) \frac{3}{2}$

Cancel the common factor.

$n > 2 \cdot - 6 \frac{3}{2}$

Rewrite the expression.

$n > - 6 \cdot 3$

Multiply $- 6$ by $3$ .

$n > - 18$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n > - 18$

Interval Notation:

$(- 18, \infty)$