Basic Math Examples

$15 = (\frac{1}{2}) (b + 4) h$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot ((b + 4) h) = 15$ .

$\frac{1}{2} \cdot ((b + 4) h) = 15$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot ((b + 4) h)) = 2 \cdot 15$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot ((b + 4) h))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (b h + 4 h)) = 2 \cdot 15$

Step 3.1.1.2

Apply the distributive property.

$2 (\frac{1}{2} (b h) + \frac{1}{2} (4 h)) = 2 \cdot 15$

Step 3.1.1.3

Multiply $\frac{1}{2} (b h)$ .

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Step 3.1.1.3.1

Combine $b$ and $\frac{1}{2}$ .

$2 (\frac{b}{2} h + \frac{1}{2} (4 h)) = 2 \cdot 15$

Step 3.1.1.3.2

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

$2 (\frac{b h}{2} + \frac{1}{2} (4 h)) = 2 \cdot 15$

Step 3.1.1.4

Cancel the common factor of $2$ .

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Step 3.1.1.4.1

Factor $2$ out of $4 h$ .

$2 (\frac{b h}{2} + \frac{1}{2} (2 (2 h))) = 2 \cdot 15$

Step 3.1.1.4.2

Cancel the common factor.

$2 (\frac{b h}{2} + \frac{1}{2} (2 (2 h))) = 2 \cdot 15$

Step 3.1.1.4.3

Rewrite the expression.

$2 (\frac{b h}{2} + 2 h) = 2 \cdot 15$

Step 3.1.1.5

Apply the distributive property.

$2 \frac{b h}{2} + 2 (2 h) = 2 \cdot 15$

Step 3.1.1.6

Cancel the common factor of $2$ .

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Step 3.1.1.6.1

Cancel the common factor.

$2 \frac{b h}{2} + 2 (2 h) = 2 \cdot 15$

Step 3.1.1.6.2

Rewrite the expression.

$b h + 2 (2 h) = 2 \cdot 15$

Step 3.1.1.7

Multiply $2$ by $2$ .

$b h + 4 h = 2 \cdot 15$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $15$ .

$b h + 4 h = 30$

Step 4

Subtract $4 h$ from both sides of the equation.

$b h = 30 - 4 h$

Step 5

Divide each term in $b h = 30 - 4 h$ by $h$ and simplify.

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Step 5.1

Divide each term in $b h = 30 - 4 h$ by $h$ .

$\frac{b h}{h} = \frac{30}{h} + \frac{- 4 h}{h}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $h$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{b h}{h} = \frac{30}{h} + \frac{- 4 h}{h}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{30}{h} + \frac{- 4 h}{h}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $h$ .

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Step 5.3.1.1

Cancel the common factor.

$b = \frac{30}{h} + \frac{- 4 h}{h}$

Step 5.3.1.2

Divide $- 4$ by $1$ .

$b = \frac{30}{h} - 4$