Finite Math Examples

$\frac{4}{3} v - \frac{4}{3} = \frac{3}{4} v - 3$

Step 1

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

$\frac{4 v}{3} - \frac{4}{3} = \frac{3}{4} v - 3$

Step 2

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

$\frac{4 v}{3} - \frac{4}{3} = \frac{3 v}{4} - 3$

Step 3

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

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Step 3.1

Subtract $\frac{3 v}{4}$ from both sides of the equation.

$\frac{4 v}{3} - \frac{4}{3} - \frac{3 v}{4} = - 3$

Step 3.2

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

$\frac{4 v}{3} \cdot \frac{4}{4} - \frac{3 v}{4} - \frac{4}{3} = - 3$

Step 3.3

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

$\frac{4 v}{3} \cdot \frac{4}{4} - \frac{3 v}{4} \cdot \frac{3}{3} - \frac{4}{3} = - 3$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

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

$\frac{4 v \cdot 4}{3 \cdot 4} - \frac{3 v}{4} \cdot \frac{3}{3} - \frac{4}{3} = - 3$

Step 3.4.2

Multiply $3$ by $4$ .

$\frac{4 v \cdot 4}{12} - \frac{3 v}{4} \cdot \frac{3}{3} - \frac{4}{3} = - 3$

Step 3.4.3

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

$\frac{4 v \cdot 4}{12} - \frac{3 v \cdot 3}{4 \cdot 3} - \frac{4}{3} = - 3$

Step 3.4.4

Multiply $4$ by $3$ .

$\frac{4 v \cdot 4}{12} - \frac{3 v \cdot 3}{12} - \frac{4}{3} = - 3$

Step 3.5

Combine the numerators over the common denominator.

$\frac{4 v \cdot 4 - 3 v \cdot 3}{12} - \frac{4}{3} = - 3$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

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

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Step 3.6.1.1.1

Factor $v$ out of $4 v \cdot 4$ .

$\frac{v (4 \cdot 4) - 3 v \cdot 3}{12} - \frac{4}{3} = - 3$

Step 3.6.1.1.2

Factor $v$ out of $- 3 v \cdot 3$ .

$\frac{v (4 \cdot 4) + v (- 3 \cdot 3)}{12} - \frac{4}{3} = - 3$

Step 3.6.1.1.3

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

$\frac{v (4 \cdot 4 - 3 \cdot 3)}{12} - \frac{4}{3} = - 3$

Step 3.6.1.2

Multiply $4$ by $4$ .

$\frac{v (16 - 3 \cdot 3)}{12} - \frac{4}{3} = - 3$

Step 3.6.1.3

Multiply $- 3$ by $3$ .

$\frac{v (16 - 9)}{12} - \frac{4}{3} = - 3$

Step 3.6.1.4

Subtract $9$ from $16$ .

$\frac{v \cdot 7}{12} - \frac{4}{3} = - 3$

Step 3.6.2

Move $7$ to the left of $v$ .

$\frac{7 v}{12} - \frac{4}{3} = - 3$

Step 4

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

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Step 4.1

Add $\frac{4}{3}$ to both sides of the equation.

$\frac{7 v}{12} = - 3 + \frac{4}{3}$

Step 4.2

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

$\frac{7 v}{12} = - 3 \cdot \frac{3}{3} + \frac{4}{3}$

Step 4.3

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

$\frac{7 v}{12} = \frac{- 3 \cdot 3}{3} + \frac{4}{3}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{7 v}{12} = \frac{- 3 \cdot 3 + 4}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $3$ .

$\frac{7 v}{12} = \frac{- 9 + 4}{3}$

Step 4.5.2

Add $- 9$ and $4$ .

$\frac{7 v}{12} = \frac{- 5}{3}$

Step 4.6

Move the negative in front of the fraction.

$\frac{7 v}{12} = - \frac{5}{3}$

Step 5

Multiply both sides of the equation by $\frac{12}{7}$ .

$\frac{12}{7} \cdot \frac{7 v}{12} = \frac{12}{7} (- \frac{5}{3})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{12}{7} \cdot \frac{7 v}{12}$ .

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Step 6.1.1.1

Cancel the common factor of $12$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{12}{7} \cdot \frac{7 v}{12} = \frac{12}{7} (- \frac{5}{3})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 v) = \frac{12}{7} (- \frac{5}{3})$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $7 v$ .

$\frac{1}{7} (7 (v)) = \frac{12}{7} (- \frac{5}{3})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 v) = \frac{12}{7} (- \frac{5}{3})$

Step 6.1.1.2.3

Rewrite the expression.

$v = \frac{12}{7} (- \frac{5}{3})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{12}{7} (- \frac{5}{3})$ .

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Step 6.2.1.1

Cancel the common factor of $3$ .

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Step 6.2.1.1.1

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

$v = \frac{12}{7} \cdot \frac{- 5}{3}$

Step 6.2.1.1.2

Factor $3$ out of $12$ .

$v = \frac{3 (4)}{7} \cdot \frac{- 5}{3}$

Step 6.2.1.1.3

Cancel the common factor.

$v = \frac{3 \cdot 4}{7} \cdot \frac{- 5}{3}$

Step 6.2.1.1.4

Rewrite the expression.

$v = \frac{4}{7} \cdot - 5$

Step 6.2.1.2

Combine $\frac{4}{7}$ and $- 5$ .

$v = \frac{4 \cdot - 5}{7}$

Step 6.2.1.3

Simplify the expression.

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Step 6.2.1.3.1

Multiply $4$ by $- 5$ .

$v = \frac{- 20}{7}$

Step 6.2.1.3.2

Move the negative in front of the fraction.

$v = - \frac{20}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{20}{7}$

Decimal Form:

$v = - 2.\overline{857142}$

Mixed Number Form:

$v = - 2 \frac{6}{7}$