Finite Math Examples

$\frac{1}{3} \cdot (3 t - 5) = \frac{t + 5}{6}$

Step 1

Multiply both sides by $6$ .

$\frac{1}{3} \cdot (3 t - 5) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{1}{3} \cdot (3 t - 5) \cdot 6$ .

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Step 2.1.1.1

Apply the distributive property.

$(\frac{1}{3} (3 t) + \frac{1}{3} \cdot - 5) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $3 t$ .

$(\frac{1}{3} (3 (t)) + \frac{1}{3} \cdot - 5) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.2.2

Cancel the common factor.

$(\frac{1}{3} (3 t) + \frac{1}{3} \cdot - 5) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.2.3

Rewrite the expression.

$(t + \frac{1}{3} \cdot - 5) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.3

Combine $\frac{1}{3}$ and $- 5$ .

$(t + \frac{- 5}{3}) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.4

Move the negative in front of the fraction.

$(t - \frac{5}{3}) \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.5

Apply the distributive property.

$t \cdot 6 - \frac{5}{3} \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.6

Move $6$ to the left of $t$ .

$6 \cdot t - \frac{5}{3} \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$6 \cdot t + \frac{- 5}{3} \cdot 6 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.7.2

Factor $3$ out of $6$ .

$6 \cdot t + \frac{- 5}{3} \cdot (3 (2)) = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.7.3

Cancel the common factor.

$6 \cdot t + \frac{- 5}{3} \cdot (3 \cdot 2) = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.7.4

Rewrite the expression.

$6 \cdot t - 5 \cdot 2 = \frac{t + 5}{6} \cdot 6$

Step 2.1.1.8

Multiply $- 5$ by $2$ .

$6 t - 10 = \frac{t + 5}{6} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$6 t - 10 = \frac{t + 5}{6} \cdot 6$

Step 2.2.1.2

Rewrite the expression.

$6 t - 10 = t + 5$

Step 3

Solve for $t$ .

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Step 3.1

Move all terms containing $t$ to the left side of the equation.

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Step 3.1.1

Subtract $t$ from both sides of the equation.

$6 t - 10 - t = 5$

Step 3.1.2

Subtract $t$ from $6 t$ .

$5 t - 10 = 5$

Step 3.2

Move all terms not containing $t$ to the right side of the equation.

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Step 3.2.1

Add $10$ to both sides of the equation.

$5 t = 5 + 10$

Step 3.2.2

Add $5$ and $10$ .

$5 t = 15$

Step 3.3

Divide each term in $5 t = 15$ by $5$ and simplify.

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Step 3.3.1

Divide each term in $5 t = 15$ by $5$ .

$\frac{5 t}{5} = \frac{15}{5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{5 t}{5} = \frac{15}{5}$

Step 3.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{15}{5}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $15$ by $5$ .

$t = 3$