Algebra Examples

$a = \frac{1}{2} (b - c)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (b - c) = a$ .

$\frac{1}{2} \cdot (b - c) = a$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (b - c)) = 2 a$

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

$2 (\frac{1}{2} b + \frac{1}{2} (- c)) = 2 a$

Step 3.1.2

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

$2 (\frac{b}{2} + \frac{1}{2} (- c)) = 2 a$

Step 3.1.3

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

$2 (\frac{b}{2} - \frac{c}{2}) = 2 a$

Step 3.1.4

Apply the distributive property.

$2 \frac{b}{2} + 2 (- \frac{c}{2}) = 2 a$

Step 3.1.5

Cancel the common factor of $2$ .

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Step 3.1.5.1

Cancel the common factor.

$2 \frac{b}{2} + 2 (- \frac{c}{2}) = 2 a$

Step 3.1.5.2

Rewrite the expression.

$b + 2 (- \frac{c}{2}) = 2 a$

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Move the leading negative in $- \frac{c}{2}$ into the numerator.

$b + 2 \frac{- c}{2} = 2 a$

Step 3.1.6.2

Cancel the common factor.

$b + 2 \frac{- c}{2} = 2 a$

Step 3.1.6.3

Rewrite the expression.

$b - c = 2 a$

Step 4

Add $c$ to both sides of the equation.

$b = 2 a + c$