Solve 9h-7(2-h)<8(h+11)+8

$$9 h - 7 ( 2 - h ) < 8 ( h + 11 ) + 8$$

Solve for h

$$h<\frac{55}{4}$$

Solution Steps

Use the distributive property to multiply -7 by 2-h.

$$9h-14+7h<8\left(h+11\right)+8$$

Combine 9h and 7h to get 16h.

$$16h-14<8\left(h+11\right)+8$$

Use the distributive property to multiply 8 by h+11.

$$16h-14<8h+88+8$$

Add 88 and 8 to get 96.

$$16h-14<8h+96$$

Subtract 8h from both sides.

$$16h-14-8h<96$$

Combine 16h and -8h to get 8h.

$$8h-14<96$$

Add 14 to both sides.

$$8h<96+14$$

Add 96 and 14 to get 110.

$$8h<110$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$h<\frac{110}{8}$$

Reduce the fraction \frac{110}{8} to lowest terms by extracting and canceling out 2.

$$h<\frac{55}{4}$$