Solve the Inequality for h (3/2)h+12>=6

$(\frac{3}{2}) h + 12 \geq 6$

Step 1

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

$\frac{3 h}{2} + 12 \geq 6$

Step 2

Move all terms not containing $h$ to the right side of the inequality.

Subtract $12$ from both sides of the inequality.

$\frac{3 h}{2} \geq 6 - 12$

Subtract $12$ from $6$ .

$\frac{3 h}{2} \geq - 6$

Step 3

Multiply both sides by $2$ .

$\frac{3 h}{2} \cdot 2 \geq - 6 \cdot 2$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 h}{2} \cdot 2 \geq - 6 \cdot 2$

Rewrite the expression.

$3 h \geq - 6 \cdot 2$

Simplify the right side.

Multiply $- 6$ by $2$ .

$3 h \geq - 12$

Step 5

Divide each term in $3 h \geq - 12$ by $3$ and simplify.

Divide each term in $3 h \geq - 12$ by $3$ .

$\frac{3 h}{3} \geq \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 h}{3} \geq \frac{- 12}{3}$

Divide $h$ by $1$ .

$h \geq \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$h \geq - 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$h \geq - 4$

Interval Notation:

$[- 4, \infty)$