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

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

Step 1

Simplify $9 h - 7 (2 - h)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 7$ by $2$ .

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

Multiply $- 1$ by $- 7$ .

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

Add $9 h$ and $7 h$ .

$16 h - 14 < 8 (h + 11) + 8 h$

Step 2

Simplify $8 (h + 11) + 8 h$ .

Simplify each term.

Apply the distributive property.

$16 h - 14 < 8 h + 8 \cdot 11 + 8 h$

Multiply $8$ by $11$ .

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

Add $8 h$ and $8 h$ .

$16 h - 14 < 16 h + 88$

Step 3

Move all terms containing $h$ to the left side of the inequality.

Subtract $16 h$ from both sides of the inequality.

$16 h - 14 - 16 h < 88$

Combine the opposite terms in $16 h - 14 - 16 h$ .

Subtract $16 h$ from $16 h$ .

$0 - 14 < 88$

Subtract $14$ from $0$ .

$- 14 < 88$

Step 4

Since $- 14 < 88$ , the inequality will always be true.

Always true

Step 5

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$