Algebra Examples

$R = \frac{1}{3} s (a - b)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (s (a - b)) = R$ .

$\frac{1}{3} \cdot (s (a - b)) = R$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (s (a - b))) = 3 R$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (s (a - b)))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} \cdot (s a + s (- b))) = 3 R$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$3 (\frac{1}{3} \cdot (s a - s b)) = 3 R$

Step 3.1.3

Apply the distributive property.

$3 (\frac{1}{3} (s a) + \frac{1}{3} (- s b)) = 3 R$

Step 3.1.4

Multiply $\frac{1}{3} (s a)$ .

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Step 3.1.4.1

Combine $s$ and $\frac{1}{3}$ .

$3 (\frac{s}{3} a + \frac{1}{3} (- s b)) = 3 R$

Step 3.1.4.2

Combine $\frac{s}{3}$ and $a$ .

$3 (\frac{s a}{3} + \frac{1}{3} (- s b)) = 3 R$

Step 3.1.5

Multiply $\frac{1}{3} (- s b)$ .

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Step 3.1.5.1

Combine $\frac{1}{3}$ and $s$ .

$3 (\frac{s a}{3} - \frac{s}{3} b) = 3 R$

Step 3.1.5.2

Combine $b$ and $\frac{s}{3}$ .

$3 (\frac{s a}{3} - \frac{b s}{3}) = 3 R$

Step 3.1.6

Apply the distributive property.

$3 \frac{s a}{3} + 3 (- \frac{b s}{3}) = 3 R$

Step 3.1.7

Cancel the common factor of $3$ .

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Step 3.1.7.1

Cancel the common factor.

$3 \frac{s a}{3} + 3 (- \frac{b s}{3}) = 3 R$

Step 3.1.7.2

Rewrite the expression.

$s a + 3 (- \frac{b s}{3}) = 3 R$

Step 3.1.8

Cancel the common factor of $3$ .

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Step 3.1.8.1

Move the leading negative in $- \frac{b s}{3}$ into the numerator.

$s a + 3 \frac{- b s}{3} = 3 R$

Step 3.1.8.2

Cancel the common factor.

$s a + 3 \frac{- b s}{3} = 3 R$

Step 3.1.8.3

Rewrite the expression.

$s a - b s = 3 R$

Step 4

Add $b s$ to both sides of the equation.

$s a = 3 R + b s$

Step 5

Divide each term in $s a = 3 R + b s$ by $s$ and simplify.

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Step 5.1

Divide each term in $s a = 3 R + b s$ by $s$ .

$\frac{s a}{s} = \frac{3 R}{s} + \frac{b s}{s}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $s$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{s a}{s} = \frac{3 R}{s} + \frac{b s}{s}$

Step 5.2.1.2

Divide $a$ by $1$ .

$a = \frac{3 R}{s} + \frac{b s}{s}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $s$ .

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Step 5.3.1.1

Cancel the common factor.

$a = \frac{3 R}{s} + \frac{b s}{s}$

Step 5.3.1.2

Divide $b$ by $1$ .

$a = \frac{3 R}{s} + b$