Algebra Examples

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Apply the distributive property.

$2 (\frac{1}{2} (h b) + \frac{1}{2} (h c)) = 2 A$

Step 3.1.3

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

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Step 3.1.3.1

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

$2 (\frac{h}{2} b + \frac{1}{2} (h c)) = 2 A$

Step 3.1.3.2

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

$2 (\frac{h b}{2} + \frac{1}{2} (h c)) = 2 A$

$2 (\frac{h b}{2} + \frac{1}{2} (h c)) = 2 A$

Step 3.1.4

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

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Step 3.1.4.1

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

$2 (\frac{h b}{2} + \frac{h}{2} c) = 2 A$

Step 3.1.4.2

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

$2 (\frac{h b}{2} + \frac{h c}{2}) = 2 A$

$2 (\frac{h b}{2} + \frac{h c}{2}) = 2 A$

Step 3.1.5

Apply the distributive property.

$2 \frac{h b}{2} + 2 \frac{h c}{2} = 2 A$

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

$2 \frac{h b}{2} + 2 \frac{h c}{2} = 2 A$

Step 3.1.6.2

Rewrite the expression.

$h b + 2 \frac{h c}{2} = 2 A$

$h b + 2 \frac{h c}{2} = 2 A$

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

Cancel the common factor.

$h b + 2 \frac{h c}{2} = 2 A$

Step 3.1.7.2

Rewrite the expression.

$h b + h c = 2 A$

$h b + h c = 2 A$

$h b + h c = 2 A$

$h b + h c = 2 A$

Step 4

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

$h b = 2 A - h c$

Step 5

Divide each term in $h b = 2 A - h c$ by $h$ and simplify.

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Step 5.1

Divide each term in $h b = 2 A - h c$ by $h$ .

$\frac{h b}{h} = \frac{2 A}{h} + \frac{- h c}{h}$

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.

$\frac{h b}{h} = \frac{2 A}{h} + \frac{- h c}{h}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{2 A}{h} + \frac{- h c}{h}$

$b = \frac{2 A}{h} + \frac{- h c}{h}$

$b = \frac{2 A}{h} + \frac{- h c}{h}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $h$ .

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Step 5.3.1.1.1

Cancel the common factor.

$b = \frac{2 A}{h} + \frac{- h c}{h}$

Step 5.3.1.1.2

Divide $- 1 c$ by $1$ .

$b = \frac{2 A}{h} - 1 c$

$b = \frac{2 A}{h} - 1 c$

Step 5.3.1.2

Rewrite $- 1 c$ as $- c$ .

$b = \frac{2 A}{h} - c$

$b = \frac{2 A}{h} - c$

$b = \frac{2 A}{h} - c$

$b = \frac{2 A}{h} - c$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$