Finite Math Examples

$2 - \frac{t}{3} = \frac{t}{6}$

Step 1

Multiply both sides by $6$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(2 - \frac{t}{3}) \cdot 6$ .

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Step 2.1.1.1

Apply the distributive property.

$2 \cdot 6 - \frac{t}{3} \cdot 6 = \frac{t}{6} \cdot 6$

Step 2.1.1.2

Multiply $2$ by $6$ .

$12 - \frac{t}{3} \cdot 6 = \frac{t}{6} \cdot 6$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

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

$12 + \frac{- t}{3} \cdot 6 = \frac{t}{6} \cdot 6$

Step 2.1.1.3.2

Factor $3$ out of $6$ .

$12 + \frac{- t}{3} \cdot (3 (2)) = \frac{t}{6} \cdot 6$

Step 2.1.1.3.3

Cancel the common factor.

$12 + \frac{- t}{3} \cdot (3 \cdot 2) = \frac{t}{6} \cdot 6$

Step 2.1.1.3.4

Rewrite the expression.

$12 - t \cdot 2 = \frac{t}{6} \cdot 6$

Step 2.1.1.4

Simplify the expression.

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Step 2.1.1.4.1

Multiply $2$ by $- 1$ .

$12 - 2 t = \frac{t}{6} \cdot 6$

Step 2.1.1.4.2

Reorder $12$ and $- 2 t$ .

$- 2 t + 12 = \frac{t}{6} \cdot 6$

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.

$- 2 t + 12 = \frac{t}{6} \cdot 6$

Step 2.2.1.2

Rewrite the expression.

$- 2 t + 12 = t$

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.

$- 2 t + 12 - t = 0$

Step 3.1.2

Subtract $t$ from $- 2 t$ .

$- 3 t + 12 = 0$

Step 3.2

Subtract $12$ from both sides of the equation.

$- 3 t = - 12$

Step 3.3

Divide each term in $- 3 t = - 12$ by $- 3$ and simplify.

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Step 3.3.1

Divide each term in $- 3 t = - 12$ by $- 3$ .

$\frac{- 3 t}{- 3} = \frac{- 12}{- 3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 3 t}{- 3} = \frac{- 12}{- 3}$

Step 3.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 12}{- 3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 12$ by $- 3$ .

$t = 4$