Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

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

Step 3

Subtract $B$ from both sides of the equation.

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

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{h b}{2} = 2 (A - B)$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

$2 \frac{h b}{2} = 2 (A - B)$

Step 5.1.1.2

Rewrite the expression.

$h b = 2 (A - B)$

$h b = 2 (A - B)$

$h b = 2 (A - B)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $2 (A - B)$ .

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Step 5.2.1.1

Apply the distributive property.

$h b = 2 A + 2 (- B)$

Step 5.2.1.2

Multiply $- 1$ by $2$ .

$h b = 2 A - 2 B$

$h b = 2 A - 2 B$

$h b = 2 A - 2 B$

$h b = 2 A - 2 B$

Step 6

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

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Step 6.1

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

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $h$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $b$ by $1$ .

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

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

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

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

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

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

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