Algebra Examples

$2 > 8 - \frac{4}{3} h$

Step 1

Rewrite so $h$ is on the left side of the inequality.

$8 - \frac{4}{3} h < 2$

Step 2

Simplify each term.

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Step 2.1

Combine $h$ and $\frac{4}{3}$ .

$8 - \frac{h \cdot 4}{3} < 2$

Step 2.2

Move $4$ to the left of $h$ .

$8 - \frac{4 h}{3} < 2$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the inequality.

$- \frac{4 h}{3} < 2 - 8$

Step 3.2

Subtract $8$ from $2$ .

$- \frac{4 h}{3} < - 6$

Step 4

Divide each term in $- \frac{4 h}{3} < - 6$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- \frac{4 h}{3} < - 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{4 h}{3}}{- 1} > \frac{- 6}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{4 h}{3}}{1} > \frac{- 6}{- 1}$

Step 4.2.2

Divide $\frac{4 h}{3}$ by $1$ .

$\frac{4 h}{3} > \frac{- 6}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 6$ by $- 1$ .

$\frac{4 h}{3} > 6$

Step 5

Multiply both sides by $3$ .

$\frac{4 h}{3} \cdot 3 > 6 \cdot 3$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1

Cancel the common factor.

$\frac{4 h}{3} \cdot 3 > 6 \cdot 3$

Step 6.1.1.2

Rewrite the expression.

$4 h > 6 \cdot 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $6$ by $3$ .

$4 h > 18$

Step 7

Divide each term in $4 h > 18$ by $4$ and simplify.

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Step 7.1

Divide each term in $4 h > 18$ by $4$ .

$\frac{4 h}{4} > \frac{18}{4}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $4$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{4 h}{4} > \frac{18}{4}$

Step 7.2.1.2

Divide $h$ by $1$ .

$h > \frac{18}{4}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Cancel the common factor of $18$ and $4$ .

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Step 7.3.1.1

Factor $2$ out of $18$ .

$h > \frac{2 (9)}{4}$

Step 7.3.1.2

Cancel the common factors.

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Step 7.3.1.2.1

Factor $2$ out of $4$ .

$h > \frac{2 \cdot 9}{2 \cdot 2}$

Step 7.3.1.2.2

Cancel the common factor.

$h > \frac{2 \cdot 9}{2 \cdot 2}$

Step 7.3.1.2.3

Rewrite the expression.

$h > \frac{9}{2}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$h > \frac{9}{2}$

Interval Notation:

$(\frac{9}{2}, \infty)$