Algebra Examples

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

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

Step 1

Rewrite the equation as

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

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

\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

$3$ .

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

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

Step 3

Simplify the left side.

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Step 3.1

Simplify

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

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

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Step 3.1.1

Apply the distributive property.

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

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

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

Step 3.1.3

Apply the distributive property.

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

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

Step 3.1.4

Multiply

\frac{1}{3} (s a)

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

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Step 3.1.4.1

Combine

s

$s$ and

\frac{1}{3}

$\frac{1}{3}$ .

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

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

Step 3.1.4.2

Combine

\frac{s}{3}

$\frac{s}{3}$ and

a

$a$ .

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

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

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

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

Step 3.1.5

Multiply

\frac{1}{3} (- s b)

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

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Step 3.1.5.1

Combine

\frac{1}{3}

$\frac{1}{3}$ and

s

$s$ .

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

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

Step 3.1.5.2

Combine

b

$b$ and

\frac{s}{3}

$\frac{s}{3}$ .

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

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

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

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

Step 3.1.6

Apply the distributive property.

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

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

Step 3.1.7

Cancel the common factor of

3

$3$ .

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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

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

Step 3.1.7.2

Rewrite the expression.

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

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

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

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

Step 3.1.8

Cancel the common factor of

3

$3$ .

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Step 3.1.8.1

Move the leading negative in

- \frac{b s}{3}

$- \frac{b s}{3}$ into the numerator.

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

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

Step 3.1.8.2

Cancel the common factor.

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

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

Step 3.1.8.3

Rewrite the expression.

s a - b s = 3 R

$s a - b s = 3 R$

s a - b s = 3 R

$s a - b s = 3 R$

s a - b s = 3 R

$s a - b s = 3 R$

s a - b s = 3 R

$s a - b s = 3 R$

Step 4

Add

b s

$b s$ to both sides of the equation.

s a = 3 R + b s

$s a = 3 R + b s$

Step 5

Divide each term in

s a = 3 R + b s

$s a = 3 R + b s$ by

s

$s$ and simplify.

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Step 5.1

Divide each term in

s a = 3 R + b s

$s a = 3 R + b s$ by

s

$s$ .

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

$s$ .

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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}

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

Step 5.2.1.2

Divide

a

$a$ by

1

$1$ .

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

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

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

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

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

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of

s

$s$ .

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Step 5.3.1.1

Cancel the common factor.

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

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

Step 5.3.1.2

Divide

b

$b$ by

1

$1$ .

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

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

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

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

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

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

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

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