Solve the Inequality for h 4-(9h-4)<8h-8+7

$4 - (9 h - 4) < 8 h - 8 + 7$

Step 1

Simplify $4 - (9 h - 4)$ .

Simplify each term.

Apply the distributive property.

$4 - (9 h) - - 4 < 8 h - 8 + 7$

Multiply $9$ by $- 1$ .

$4 - 9 h - - 4 < 8 h - 8 + 7$

Multiply $- 1$ by $- 4$ .

$4 - 9 h + 4 < 8 h - 8 + 7$

Add $4$ and $4$ .

$- 9 h + 8 < 8 h - 8 + 7$

Step 2

Add $- 8$ and $7$ .

$- 9 h + 8 < 8 h - 1$

Step 3

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

Subtract $8 h$ from both sides of the inequality.

$- 9 h + 8 - 8 h < - 1$

Subtract $8 h$ from $- 9 h$ .

$- 17 h + 8 < - 1$

Step 4

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

Subtract $8$ from both sides of the inequality.

$- 17 h < - 1 - 8$

Subtract $8$ from $- 1$ .

$- 17 h < - 9$

Step 5

Divide each term in $- 17 h < - 9$ by $- 17$ and simplify.

Divide each term in $- 17 h < - 9$ by $- 17$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 17 h}{- 17} > \frac{- 9}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 h}{- 17} > \frac{- 9}{- 17}$

Divide $h$ by $1$ .

$h > \frac{- 9}{- 17}$

Simplify the right side.

Dividing two negative values results in a positive value.

$h > \frac{9}{17}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$h > \frac{9}{17}$

Interval Notation:

$(\frac{9}{17}, \infty)$

Solve the Inequality for h 4-(9h-4)<8h-8+7

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