Basic Math Examples

$\frac{1}{5} \cdot (4 t - 6) = \frac{11}{5} t - \frac{t + 6}{10}$

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.

$\frac{11}{5} t - \frac{t + 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2

Simplify $\frac{11}{5} t - \frac{t + 6}{10}$ .

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Step 2.1

Combine $\frac{11}{5}$ and $t$ .

$\frac{11 t}{5} - \frac{t + 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.2

To write $\frac{11 t}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 t}{5} \cdot \frac{2}{2} - \frac{t + 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{11 t}{5}$ by $\frac{2}{2}$ .

$\frac{11 t \cdot 2}{5 \cdot 2} - \frac{t + 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{11 t \cdot 2}{10} - \frac{t + 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.4

Combine the numerators over the common denominator.

$\frac{11 t \cdot 2 - (t + 6)}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $11$ .

$\frac{22 t - (t + 6)}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5.2

Apply the distributive property.

$\frac{22 t - t - 1 \cdot 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5.3

Multiply $- 1$ by $6$ .

$\frac{22 t - t - 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5.4

Subtract $t$ from $22 t$ .

$\frac{21 t - 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5.5

Factor $3$ out of $21 t - 6$ .

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Step 2.5.5.1

Factor $3$ out of $21 t$ .

$\frac{3 (7 t) - 6}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5.5.2

Factor $3$ out of $- 6$ .

$\frac{3 (7 t) + 3 (- 2)}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 2.5.5.3

Factor $3$ out of $3 (7 t) + 3 (- 2)$ .

$\frac{3 (7 t - 2)}{10} = \frac{1}{5} \cdot (4 t - 6)$

Step 3

Simplify $\frac{1}{5} \cdot (4 t - 6)$ .

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Step 3.1

Apply the distributive property.

$\frac{3 (7 t - 2)}{10} = \frac{1}{5} (4 t) + \frac{1}{5} \cdot - 6$

Step 3.2

Multiply $\frac{1}{5} (4 t)$ .

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Step 3.2.1

Combine $4$ and $\frac{1}{5}$ .

$\frac{3 (7 t - 2)}{10} = \frac{4}{5} t + \frac{1}{5} \cdot - 6$

Step 3.2.2

Combine $\frac{4}{5}$ and $t$ .

$\frac{3 (7 t - 2)}{10} = \frac{4 t}{5} + \frac{1}{5} \cdot - 6$

Step 3.3

Combine $\frac{1}{5}$ and $- 6$ .

$\frac{3 (7 t - 2)}{10} = \frac{4 t}{5} + \frac{- 6}{5}$

Step 3.4

Move the negative in front of the fraction.

$\frac{3 (7 t - 2)}{10} = \frac{4 t}{5} - \frac{6}{5}$

Step 4

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

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Step 4.1

Subtract $\frac{4 t}{5}$ from both sides of the equation.

$\frac{3 (7 t - 2)}{10} - \frac{4 t}{5} = - \frac{6}{5}$

Step 4.2

To write $- \frac{4 t}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 (7 t - 2)}{10} - \frac{4 t}{5} \cdot \frac{2}{2} = - \frac{6}{5}$

Step 4.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{4 t}{5}$ by $\frac{2}{2}$ .

$\frac{3 (7 t - 2)}{10} - \frac{4 t \cdot 2}{5 \cdot 2} = - \frac{6}{5}$

Step 4.3.2

Multiply $5$ by $2$ .

$\frac{3 (7 t - 2)}{10} - \frac{4 t \cdot 2}{10} = - \frac{6}{5}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{3 (7 t - 2) - 4 t \cdot 2}{10} = - \frac{6}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Apply the distributive property.

$\frac{3 (7 t) + 3 \cdot - 2 - 4 t \cdot 2}{10} = - \frac{6}{5}$

Step 4.5.2

Multiply $7$ by $3$ .

$\frac{21 t + 3 \cdot - 2 - 4 t \cdot 2}{10} = - \frac{6}{5}$

Step 4.5.3

Multiply $3$ by $- 2$ .

$\frac{21 t - 6 - 4 t \cdot 2}{10} = - \frac{6}{5}$

Step 4.5.4

Multiply $2$ by $- 4$ .

$\frac{21 t - 6 - 8 t}{10} = - \frac{6}{5}$

Step 4.5.5

Subtract $8 t$ from $21 t$ .

$\frac{13 t - 6}{10} = - \frac{6}{5}$

Step 5

Multiply both sides by $10$ .

$\frac{13 t - 6}{10} \cdot 10 = - \frac{6}{5} \cdot 10$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1

Cancel the common factor.

$\frac{13 t - 6}{10} \cdot 10 = - \frac{6}{5} \cdot 10$

Step 6.1.1.2

Rewrite the expression.

$13 t - 6 = - \frac{6}{5} \cdot 10$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{6}{5} \cdot 10$ .

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Step 6.2.1.1

Cancel the common factor of $5$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$13 t - 6 = \frac{- 6}{5} \cdot 10$

Step 6.2.1.1.2

Factor $5$ out of $10$ .

$13 t - 6 = \frac{- 6}{5} \cdot (5 (2))$

Step 6.2.1.1.3

Cancel the common factor.

$13 t - 6 = \frac{- 6}{5} \cdot (5 \cdot 2)$

Step 6.2.1.1.4

Rewrite the expression.

$13 t - 6 = - 6 \cdot 2$

Step 6.2.1.2

Multiply $- 6$ by $2$ .

$13 t - 6 = - 12$

Step 7

Solve for $t$ .

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Step 7.1

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

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Step 7.1.1

Add $6$ to both sides of the equation.

$13 t = - 12 + 6$

Step 7.1.2

Add $- 12$ and $6$ .

$13 t = - 6$

Step 7.2

Divide each term in $13 t = - 6$ by $13$ and simplify.

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Step 7.2.1

Divide each term in $13 t = - 6$ by $13$ .

$\frac{13 t}{13} = \frac{- 6}{13}$

Step 7.2.2

Simplify the left side.

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Step 7.2.2.1

Cancel the common factor of $13$ .

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Step 7.2.2.1.1

Cancel the common factor.

$\frac{13 t}{13} = \frac{- 6}{13}$

Step 7.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 6}{13}$

Step 7.2.3

Simplify the right side.

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Step 7.2.3.1

Move the negative in front of the fraction.

$t = - \frac{6}{13}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{6}{13}$

Decimal Form:

$t = - 0.\overline{461538}$