Algebra Examples

$r = \frac{1}{3} \cdot (d (60 - t))$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (d (60 - t)) = r$ .

$\frac{1}{3} \cdot (d (60 - t)) = r$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (d (60 - t))) = 3 r$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (d (60 - t)))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} \cdot (d \cdot 60 + d (- t))) = 3 r$

Step 3.1.2

Reorder.

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Step 3.1.2.1

Move $60$ to the left of $d$ .

$3 (\frac{1}{3} \cdot (60 \cdot d + d (- t))) = 3 r$

Step 3.1.2.2

Rewrite using the commutative property of multiplication.

$3 (\frac{1}{3} \cdot (60 \cdot d - d t)) = 3 r$

Step 3.1.3

Apply the distributive property.

$3 (\frac{1}{3} (60 d) + \frac{1}{3} (- d t)) = 3 r$

Step 3.1.4

Cancel the common factor of $3$ .

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Step 3.1.4.1

Factor $3$ out of $60 d$ .

$3 (\frac{1}{3} (3 (20 d)) + \frac{1}{3} (- d t)) = 3 r$

Step 3.1.4.2

Cancel the common factor.

$3 (\frac{1}{3} (3 (20 d)) + \frac{1}{3} (- d t)) = 3 r$

Step 3.1.4.3

Rewrite the expression.

$3 (20 d + \frac{1}{3} (- d t)) = 3 r$

Step 3.1.5

Multiply $\frac{1}{3} (- d t)$ .

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Step 3.1.5.1

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

$3 (20 d - \frac{d}{3} t) = 3 r$

Step 3.1.5.2

Combine $t$ and $\frac{d}{3}$ .

$3 (20 d - \frac{t d}{3}) = 3 r$

Step 3.1.6

Apply the distributive property.

$3 (20 d) + 3 (- \frac{t d}{3}) = 3 r$

Step 3.1.7

Multiply $20$ by $3$ .

$60 d + 3 (- \frac{t d}{3}) = 3 r$

Step 3.1.8

Cancel the common factor of $3$ .

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Step 3.1.8.1

Move the leading negative in $- \frac{t d}{3}$ into the numerator.

$60 d + 3 \frac{- t d}{3} = 3 r$

Step 3.1.8.2

Cancel the common factor.

$60 d + 3 \frac{- t d}{3} = 3 r$

Step 3.1.8.3

Rewrite the expression.

$60 d - t d = 3 r$

Step 4

Subtract $60 d$ from both sides of the equation.

$- t d = 3 r - 60 d$

Step 5

Divide each term in $- t d = 3 r - 60 d$ by $- d$ and simplify.

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Step 5.1

Divide each term in $- t d = 3 r - 60 d$ by $- d$ .

$\frac{- t d}{- d} = \frac{3 r}{- d} + \frac{- 60 d}{- d}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{t d}{d} = \frac{3 r}{- d} + \frac{- 60 d}{- d}$

Step 5.2.2

Cancel the common factor of $d$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{t d}{d} = \frac{3 r}{- d} + \frac{- 60 d}{- d}$

Step 5.2.2.2

Divide $t$ by $1$ .

$t = \frac{3 r}{- d} + \frac{- 60 d}{- d}$

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.

$t = - \frac{3 r}{d} + \frac{- 60 d}{- d}$

Step 5.3.1.2

Cancel the common factor of $d$ .

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Step 5.3.1.2.1

Cancel the common factor.

$t = - \frac{3 r}{d} + \frac{- 60 d}{- d}$

Step 5.3.1.2.2

Rewrite the expression.

$t = - \frac{3 r}{d} + \frac{- 60}{- 1}$

Step 5.3.1.2.3

Move the negative one from the denominator of $\frac{- 60}{- 1}$ .

$t = - \frac{3 r}{d} - 1 \cdot - 60$

Step 5.3.1.3

Rewrite $- 1 \cdot - 60$ as $- - 60$ .

$t = - \frac{3 r}{d} - - 60$

Step 5.3.1.4

Multiply $- 1$ by $- 60$ .

$t = - \frac{3 r}{d} + 60$