Algebra Examples

$- 7 h + 2 (- 4 h + 5) > - 4 h + 1 + 10$

Step 1

Simplify $- 7 h + 2 (- 4 h + 5)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 7 h + 2 (- 4 h) + 2 \cdot 5 > - 4 h + 1 + 10$

Step 1.1.2

Multiply $- 4$ by $2$ .

$- 7 h - 8 h + 2 \cdot 5 > - 4 h + 1 + 10$

Step 1.1.3

Multiply $2$ by $5$ .

$- 7 h - 8 h + 10 > - 4 h + 1 + 10$

Step 1.2

Subtract $8 h$ from $- 7 h$ .

$- 15 h + 10 > - 4 h + 1 + 10$

Step 2

Add $1$ and $10$ .

$- 15 h + 10 > - 4 h + 11$

Step 3

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

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Step 3.1

Add $4 h$ to both sides of the inequality.

$- 15 h + 10 + 4 h > 11$

Step 3.2

Add $- 15 h$ and $4 h$ .

$- 11 h + 10 > 11$

Step 4

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

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Step 4.1

Subtract $10$ from both sides of the inequality.

$- 11 h > 11 - 10$

Step 4.2

Subtract $10$ from $11$ .

$- 11 h > 1$

Step 5

Divide each term in $- 11 h > 1$ by $- 11$ and simplify.

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Step 5.1

Divide each term in $- 11 h > 1$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 11 h}{- 11} < \frac{1}{- 11}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 11$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 11 h}{- 11} < \frac{1}{- 11}$

Step 5.2.1.2

Divide $h$ by $1$ .

$h < \frac{1}{- 11}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$h < - \frac{1}{11}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$h < - \frac{1}{11}$

Interval Notation:

$(- \infty, - \frac{1}{11})$