Algebra Examples

$a > (w h) + 0.5 (b h)$

Step 1

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

$w h + 0.5 b h < a$

Step 2

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

$0.5 b h < a - w h$

Step 3

Divide each term in $0.5 b h < a - w h$ by $0.5 h$ and simplify.

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Step 3.1

Divide each term in $0.5 b h < a - w h$ by $0.5 h$ .

$\frac{0.5 b h}{0.5 h} < \frac{a}{0.5 h} + \frac{- w h}{0.5 h}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.5 b h}{0.5 h} < \frac{a}{0.5 h} + \frac{- w h}{0.5 h}$

Step 3.2.1.2

Rewrite the expression.

$\frac{b h}{h} < \frac{a}{0.5 h} + \frac{- w h}{0.5 h}$

Step 3.2.2

Cancel the common factor of $h$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{b h}{h} < \frac{a}{0.5 h} + \frac{- w h}{0.5 h}$

Step 3.2.2.2

Divide $b$ by $1$ .

$b < \frac{a}{0.5 h} + \frac{- w h}{0.5 h}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply by $1$ .

$b < \frac{1 a}{0.5 h} + \frac{- w h}{0.5 h}$

Step 3.3.1.2

Factor $0.5$ out of $0.5 h$ .

$b < \frac{1 a}{0.5 (h)} + \frac{- w h}{0.5 h}$

Step 3.3.1.3

Separate fractions.

$b < \frac{1}{0.5} \cdot \frac{a}{h} + \frac{- w h}{0.5 h}$

Step 3.3.1.4

Divide $1$ by $0.5$ .

$b < 2 \frac{a}{h} + \frac{- w h}{0.5 h}$

Step 3.3.1.5

Combine $2$ and $\frac{a}{h}$ .

$b < \frac{2 a}{h} + \frac{- w h}{0.5 h}$

Step 3.3.1.6

Cancel the common factor of $h$ .

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Step 3.3.1.6.1

Cancel the common factor.

$b < \frac{2 a}{h} + \frac{- w h}{0.5 h}$

Step 3.3.1.6.2

Rewrite the expression.

$b < \frac{2 a}{h} + \frac{- w}{0.5}$

Step 3.3.1.7

Move the negative in front of the fraction.

$b < \frac{2 a}{h} - \frac{w}{0.5}$

Step 3.3.1.8

Multiply by $1$ .

$b < \frac{2 a}{h} - \frac{1 w}{0.5}$

Step 3.3.1.9

Factor $0.5$ out of $0.5$ .

$b < \frac{2 a}{h} - \frac{1 w}{0.5 (1)}$

Step 3.3.1.10

Separate fractions.

$b < \frac{2 a}{h} - (\frac{1}{0.5} \cdot \frac{w}{1})$

Step 3.3.1.11

Divide $1$ by $0.5$ .

$b < \frac{2 a}{h} - (2 \frac{w}{1})$

Step 3.3.1.12

Divide $w$ by $1$ .

$b < \frac{2 a}{h} - (2 w)$

Step 3.3.1.13

Multiply $2$ by $- 1$ .

$b < \frac{2 a}{h} - 2 w$