Algebra Examples

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Apply the distributive property.

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

Step 3.1.3

Multiply $\frac{1}{2} (a x)$ .

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Step 3.1.3.1

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

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

Step 3.1.3.2

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

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

Step 3.1.4

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

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Step 3.1.4.1

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

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

Step 3.1.4.2

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

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

Step 3.1.5

Apply the distributive property.

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

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Cancel the common factor.

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

Step 3.1.6.2

Rewrite the expression.

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

Step 3.1.7

Cancel the common factor of $2$ .

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Step 3.1.7.1

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

$a x + 2 \frac{- x b}{2} = 2 S$

Step 3.1.7.2

Cancel the common factor.

$a x + 2 \frac{- x b}{2} = 2 S$

Step 3.1.7.3

Rewrite the expression.

$a x - x b = 2 S$

Step 4

Subtract $a x$ from both sides of the equation.

$- x b = 2 S - a x$

Step 5

Divide each term in $- x b = 2 S - a x$ by $- x$ and simplify.

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Step 5.1

Divide each term in $- x b = 2 S - a x$ by $- x$ .

$\frac{- x b}{- x} = \frac{2 S}{- x} + \frac{- a x}{- x}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x b}{x} = \frac{2 S}{- x} + \frac{- a x}{- x}$

Step 5.2.2

Cancel the common factor of $x$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{x b}{x} = \frac{2 S}{- x} + \frac{- a x}{- x}$

Step 5.2.2.2

Divide $b$ by $1$ .

$b = \frac{2 S}{- x} + \frac{- a x}{- x}$

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

Move the negative in front of the fraction.

$b = - \frac{2 S}{x} + \frac{- a x}{- x}$

Step 5.3.1.2

Dividing two negative values results in a positive value.

$b = - \frac{2 S}{x} + \frac{a x}{x}$

Step 5.3.1.3

Cancel the common factor of $x$ .

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Step 5.3.1.3.1

Cancel the common factor.

$b = - \frac{2 S}{x} + \frac{a x}{x}$

Step 5.3.1.3.2

Divide $a$ by $1$ .

$b = - \frac{2 S}{x} + a$