Basic Math Examples

$\frac{2}{3} t - 11 = 4 (16 - t) - \frac{1}{3} t$

Step 1

Since $t$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 (16 - t) - \frac{1}{3} t = \frac{2}{3} t - 11$

Step 2

Simplify $4 (16 - t) - \frac{1}{3} t$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 \cdot 16 + 4 (- t) - \frac{1}{3} t = \frac{2}{3} t - 11$

Step 2.1.2

Multiply $4$ by $16$ .

$64 + 4 (- t) - \frac{1}{3} t = \frac{2}{3} t - 11$

Step 2.1.3

Multiply $- 1$ by $4$ .

$64 - 4 t - \frac{1}{3} t = \frac{2}{3} t - 11$

Step 2.1.4

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

$64 - 4 t - \frac{t}{3} = \frac{2}{3} t - 11$

Step 2.2

To write $- 4 t$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$64 - 4 t \cdot \frac{3}{3} - \frac{t}{3} = \frac{2}{3} t - 11$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $- 4 t$ and $\frac{3}{3}$ .

$64 + \frac{- 4 t \cdot 3}{3} - \frac{t}{3} = \frac{2}{3} t - 11$

Step 2.3.2

Combine the numerators over the common denominator.

$64 + \frac{- 4 t \cdot 3 - t}{3} = \frac{2}{3} t - 11$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $t$ out of $- 4 t \cdot 3 - t$ .

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Step 2.4.1.1.1

Factor $t$ out of $- 4 t \cdot 3$ .

$64 + \frac{t (- 4 \cdot 3) - t}{3} = \frac{2}{3} t - 11$

Step 2.4.1.1.2

Factor $t$ out of $- t$ .

$64 + \frac{t (- 4 \cdot 3) + t \cdot - 1}{3} = \frac{2}{3} t - 11$

Step 2.4.1.1.3

Factor $t$ out of $t (- 4 \cdot 3) + t \cdot - 1$ .

$64 + \frac{t (- 4 \cdot 3 - 1)}{3} = \frac{2}{3} t - 11$

Step 2.4.1.2

Multiply $- 4$ by $3$ .

$64 + \frac{t (- 12 - 1)}{3} = \frac{2}{3} t - 11$

Step 2.4.1.3

Subtract $1$ from $- 12$ .

$64 + \frac{t \cdot - 13}{3} = \frac{2}{3} t - 11$

Step 2.4.2

Move $- 13$ to the left of $t$ .

$64 + \frac{- 13 \cdot t}{3} = \frac{2}{3} t - 11$

Step 2.4.3

Move the negative in front of the fraction.

$64 - \frac{13 t}{3} = \frac{2}{3} t - 11$

Step 3

Combine $\frac{2}{3}$ and $t$ .

$64 - \frac{13 t}{3} = \frac{2 t}{3} - 11$

Step 4

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

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Step 4.1

Subtract $\frac{2 t}{3}$ from both sides of the equation.

$64 - \frac{13 t}{3} - \frac{2 t}{3} = - 11$

Step 4.2

Combine the numerators over the common denominator.

$64 + \frac{- 13 t - 2 t}{3} = - 11$

Step 4.3

Subtract $2 t$ from $- 13 t$ .

$64 + \frac{- 15 t}{3} = - 11$

Step 4.4

Cancel the common factor of $- 15$ and $3$ .

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Step 4.4.1

Factor $3$ out of $- 15 t$ .

$64 + \frac{3 (- 5 t)}{3} = - 11$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $3$ out of $3$ .

$64 + \frac{3 (- 5 t)}{3 (1)} = - 11$

Step 4.4.2.2

Cancel the common factor.

$64 + \frac{3 (- 5 t)}{3 \cdot 1} = - 11$

Step 4.4.2.3

Rewrite the expression.

$64 + \frac{- 5 t}{1} = - 11$

Step 4.4.2.4

Divide $- 5 t$ by $1$ .

$64 - 5 t = - 11$

Step 5

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

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Step 5.1

Subtract $64$ from both sides of the equation.

$- 5 t = - 11 - 64$

Step 5.2

Subtract $64$ from $- 11$ .

$- 5 t = - 75$

Step 6

Divide each term in $- 5 t = - 75$ by $- 5$ and simplify.

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Step 6.1

Divide each term in $- 5 t = - 75$ by $- 5$ .

$\frac{- 5 t}{- 5} = \frac{- 75}{- 5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 5 t}{- 5} = \frac{- 75}{- 5}$

Step 6.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 75}{- 5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 75$ by $- 5$ .

$t = 15$