Basic Math Examples

$\frac{4}{3} \cdot (t + 1) - \frac{1}{6} \cdot (4 t - 3) = 2$

Step 1

Simplify $\frac{4}{3} \cdot (t + 1) - \frac{1}{6} \cdot (4 t - 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{4}{3} t + \frac{4}{3} \cdot 1 - \frac{1}{6} \cdot (4 t - 3) = 2$

Step 1.1.2

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

$\frac{4 t}{3} + \frac{4}{3} \cdot 1 - \frac{1}{6} \cdot (4 t - 3) = 2$

Step 1.1.3

Multiply $\frac{4}{3}$ by $1$ .

$\frac{4 t}{3} + \frac{4}{3} - \frac{1}{6} \cdot (4 t - 3) = 2$

Step 1.1.4

Apply the distributive property.

$\frac{4 t}{3} + \frac{4}{3} - \frac{1}{6} (4 t) - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 1}{6} (4 t) - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.5.2

Factor $2$ out of $6$ .

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 1}{2 (3)} (4 t) - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.5.3

Factor $2$ out of $4 t$ .

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 1}{2 (3)} (2 (2 t)) - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.5.4

Cancel the common factor.

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 1}{2 \cdot 3} (2 (2 t)) - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.5.5

Rewrite the expression.

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 1}{3} (2 t) - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.6

Combine $2$ and $\frac{- 1}{3}$ .

$\frac{4 t}{3} + \frac{4}{3} + \frac{2 \cdot - 1}{3} t - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.7

Multiply $2$ by $- 1$ .

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 2}{3} t - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.8

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

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 2 t}{3} - \frac{1}{6} \cdot - 3 = 2$

Step 1.1.9

Cancel the common factor of $3$ .

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Step 1.1.9.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 2 t}{3} + \frac{- 1}{6} \cdot - 3 = 2$

Step 1.1.9.2

Factor $3$ out of $6$ .

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

Step 1.1.9.3

Factor $3$ out of $- 3$ .

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

Step 1.1.9.4

Cancel the common factor.

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

Step 1.1.9.5

Rewrite the expression.

$\frac{4 t}{3} + \frac{4}{3} + \frac{- 2 t}{3} + \frac{- 1}{2} \cdot - 1 = 2$

Step 1.1.10

Combine $\frac{- 1}{2}$ and $- 1$ .

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

Step 1.1.11

Multiply $- 1$ by $- 1$ .

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

Step 1.1.12

Move the negative in front of the fraction.

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

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

Step 1.2.2

Subtract $2 t$ from $4 t$ .

$\frac{2 t + 4}{3} + \frac{1}{2} = 2$

Step 1.2.3

Factor $2$ out of $2 t + 4$ .

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Step 1.2.3.1

Factor $2$ out of $2 t$ .

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

Step 1.2.3.2

Factor $2$ out of $4$ .

$\frac{2 t + 2 \cdot 2}{3} + \frac{1}{2} = 2$

Step 1.2.3.3

Factor $2$ out of $2 t + 2 \cdot 2$ .

$\frac{2 (t + 2)}{3} + \frac{1}{2} = 2$

Step 1.3

To write $\frac{2 (t + 2)}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 (t + 2)}{3} \cdot \frac{2}{2} + \frac{1}{2} = 2$

Step 1.4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 (t + 2)}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3} = 2$

Step 1.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.1

Multiply $\frac{2 (t + 2)}{3}$ by $\frac{2}{2}$ .

$\frac{2 (t + 2) \cdot 2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3} = 2$

Step 1.5.2

Multiply $3$ by $2$ .

$\frac{2 (t + 2) \cdot 2}{6} + \frac{1}{2} \cdot \frac{3}{3} = 2$

Step 1.5.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 1.5.4

Multiply $2$ by $3$ .

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 1.7

Simplify the numerator.

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Step 1.7.1

Apply the distributive property.

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

Step 1.7.2

Multiply $2$ by $2$ .

$\frac{(2 t + 4) \cdot 2 + 3}{6} = 2$

Step 1.7.3

Apply the distributive property.

$\frac{2 t \cdot 2 + 4 \cdot 2 + 3}{6} = 2$

Step 1.7.4

Multiply $2$ by $2$ .

$\frac{4 t + 4 \cdot 2 + 3}{6} = 2$

Step 1.7.5

Multiply $4$ by $2$ .

$\frac{4 t + 8 + 3}{6} = 2$

Step 1.7.6

Add $8$ and $3$ .

$\frac{4 t + 11}{6} = 2$

Step 2

Multiply both sides by $6$ .

$\frac{4 t + 11}{6} \cdot 6 = 2 \cdot 6$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{4 t + 11}{6} \cdot 6 = 2 \cdot 6$

Step 3.1.1.2

Rewrite the expression.

$4 t + 11 = 2 \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $6$ .

$4 t + 11 = 12$

Step 4

Solve for $t$ .

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Step 4.1

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

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Step 4.1.1

Subtract $11$ from both sides of the equation.

$4 t = 12 - 11$

Step 4.1.2

Subtract $11$ from $12$ .

$4 t = 1$

Step 4.2

Divide each term in $4 t = 1$ by $4$ and simplify.

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Step 4.2.1

Divide each term in $4 t = 1$ by $4$ .

$\frac{4 t}{4} = \frac{1}{4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{4 t}{4} = \frac{1}{4}$

Step 4.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{1}{4}$

Decimal Form:

$t = 0.25$