Algebra Examples

$- 4 (h - 10) < 7 h (2 + 3)$

Step 1

Simplify $- 4 (h - 10)$ .

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Step 1.1

Rewrite.

$0 + 0 - 4 (h - 10) < 7 h (2 + 3)$

Step 1.2

Simplify by adding zeros.

$- 4 (h - 10) < 7 h (2 + 3)$

Step 1.3

Apply the distributive property.

$- 4 h - 4 \cdot - 10 < 7 h (2 + 3)$

Step 1.4

Multiply $- 4$ by $- 10$ .

$- 4 h + 40 < 7 h (2 + 3)$

Step 2

Simplify $7 h (2 + 3)$ .

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Step 2.1

Add $2$ and $3$ .

$- 4 h + 40 < 7 h \cdot 5$

Step 2.2

Multiply $5$ by $7$ .

$- 4 h + 40 < 35 h$

Step 3

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

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Step 3.1

Subtract $35 h$ from both sides of the inequality.

$- 4 h + 40 - 35 h < 0$

Step 3.2

Subtract $35 h$ from $- 4 h$ .

$- 39 h + 40 < 0$

Step 4

Subtract $40$ from both sides of the inequality.

$- 39 h < - 40$

Step 5

Divide each term in $- 39 h < - 40$ by $- 39$ and simplify.

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Step 5.1

Divide each term in $- 39 h < - 40$ by $- 39$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 39 h}{- 39} > \frac{- 40}{- 39}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 39$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 39 h}{- 39} > \frac{- 40}{- 39}$

Step 5.2.1.2

Divide $h$ by $1$ .

$h > \frac{- 40}{- 39}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$h > \frac{40}{39}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$h > \frac{40}{39}$

Interval Notation:

$(\frac{40}{39}, \infty)$