Solve 4/5h-2/3(h-9)geq1/15(2h+90)

$$\frac { 4 } { 5 } h - \frac { 2 } { 3 } ( h - 9 ) \geq \frac { 1 } { 15 } ( 2 h + 90 )$$

Solve for h

$$h\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by h-9.

$$\frac{4}{5}h-\frac{2}{3}h-\frac{2}{3}\left(-9\right)\geq \frac{1}{15}\left(2h+90\right)$$

Express -\frac{2}{3}\left(-9\right) as a single fraction.

$$\frac{4}{5}h-\frac{2}{3}h+\frac{-2\left(-9\right)}{3}\geq \frac{1}{15}\left(2h+90\right)$$

Multiply -2 and -9 to get 18.

$$\frac{4}{5}h-\frac{2}{3}h+\frac{18}{3}\geq \frac{1}{15}\left(2h+90\right)$$

Divide 18 by 3 to get 6.

$$\frac{4}{5}h-\frac{2}{3}h+6\geq \frac{1}{15}\left(2h+90\right)$$

Combine \frac{4}{5}h and -\frac{2}{3}h to get \frac{2}{15}h.

$$\frac{2}{15}h+6\geq \frac{1}{15}\left(2h+90\right)$$

Use the distributive property to multiply \frac{1}{15} by 2h+90.

$$\frac{2}{15}h+6\geq \frac{1}{15}\times 2h+\frac{1}{15}\times 90$$

Multiply \frac{1}{15} and 2 to get \frac{2}{15}.

$$\frac{2}{15}h+6\geq \frac{2}{15}h+\frac{1}{15}\times 90$$

Multiply \frac{1}{15} and 90 to get \frac{90}{15}.

$$\frac{2}{15}h+6\geq \frac{2}{15}h+\frac{90}{15}$$

Divide 90 by 15 to get 6.

$$\frac{2}{15}h+6\geq \frac{2}{15}h+6$$

Subtract \frac{2}{15}h from both sides.

$$\frac{2}{15}h+6-\frac{2}{15}h\geq 6$$

Combine \frac{2}{15}h and -\frac{2}{15}h to get 0.

$$6\geq 6$$

This is true for any h.

$$h\in \mathrm{R}$$