Finite Math Examples

\frac{1}{3} m - \frac{5}{12} = \frac{3}{4} + \frac{1}{2} m

$\frac{1}{3} m - \frac{5}{12} = \frac{3}{4} + \frac{1}{2} m$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract

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

$\frac{1}{3} m - \frac{5}{12} - \frac{3}{4} = \frac{1}{2} m$

Step 1.2

Subtract

$\frac{1}{2} m$ from both sides of the equation.

$\frac{1}{3} m - \frac{5}{12} - \frac{3}{4} - \frac{1}{2} m = 0$

Step 2

Simplify

$\frac{1}{3} m - \frac{5}{12} - \frac{3}{4} - \frac{1}{2} m$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine

$\frac{1}{3}$ and

$m$ .

$\frac{m}{3} - \frac{5}{12} - \frac{3}{4} - \frac{1}{2} m = 0$

Step 2.1.2

Combine

$m$ and

$\frac{1}{2}$ .

$\frac{m}{3} - \frac{5}{12} - \frac{3}{4} - \frac{m}{2} = 0$

Step 2.2

To write

$\frac{m}{3}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{m}{3} \cdot \frac{2}{2} - \frac{m}{2} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.3

To write

$- \frac{m}{2}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{m}{3} \cdot \frac{2}{2} - \frac{m}{2} \cdot \frac{3}{3} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.4

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

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Step 2.4.1

Multiply

$\frac{m}{3}$ by

$\frac{2}{2}$ .

$\frac{m \cdot 2}{3 \cdot 2} - \frac{m}{2} \cdot \frac{3}{3} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.4.2

Multiply

$3$ by

$2$ .

$\frac{m \cdot 2}{6} - \frac{m}{2} \cdot \frac{3}{3} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.4.3

Multiply

$\frac{m}{2}$ by

$\frac{3}{3}$ .

$\frac{m \cdot 2}{6} - \frac{m \cdot 3}{2 \cdot 3} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.4.4

Multiply

$2$ by

$3$ .

$\frac{m \cdot 2}{6} - \frac{m \cdot 3}{6} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{m \cdot 2 - m \cdot 3}{6} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.6

Find the common denominator.

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Step 2.6.1

Multiply

$\frac{m \cdot 2 - m \cdot 3}{6}$ by

$\frac{2}{2}$ .

$\frac{m \cdot 2 - m \cdot 3}{6} \cdot \frac{2}{2} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.6.2

Multiply

$\frac{m \cdot 2 - m \cdot 3}{6}$ by

$\frac{2}{2}$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{6 \cdot 2} - \frac{5}{12} - \frac{3}{4} = 0$

Step 2.6.3

Multiply

$\frac{3}{4}$ by

$\frac{3}{3}$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{6 \cdot 2} - \frac{5}{12} - (\frac{3}{4} \cdot \frac{3}{3}) = 0$

Step 2.6.4

Multiply

$\frac{3}{4}$ by

$\frac{3}{3}$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{6 \cdot 2} - \frac{5}{12} - \frac{3 \cdot 3}{4 \cdot 3} = 0$

Step 2.6.5

Reorder the factors of

$6 \cdot 2$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{2 \cdot 6} - \frac{5}{12} - \frac{3 \cdot 3}{4 \cdot 3} = 0$

Step 2.6.6

Multiply

$2$ by

$6$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{12} - \frac{5}{12} - \frac{3 \cdot 3}{4 \cdot 3} = 0$

Step 2.6.7

Reorder the factors of

$4 \cdot 3$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{12} - \frac{5}{12} - \frac{3 \cdot 3}{3 \cdot 4} = 0$

Step 2.6.8

Multiply

$3$ by

$4$ .

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2}{12} - \frac{5}{12} - \frac{3 \cdot 3}{12} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{(m \cdot 2 - m \cdot 3) \cdot 2 - 5 - 3 \cdot 3}{12} = 0$

Step 2.8

Simplify each term.

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Step 2.8.1

Simplify each term.

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Step 2.8.1.1

Move

$2$ to the left of

$m$ .

$\frac{(2 \cdot m - m \cdot 3) \cdot 2 - 5 - 3 \cdot 3}{12} = 0$

Step 2.8.1.2

Multiply

$3$ by

$- 1$ .

$\frac{(2 m - 3 m) \cdot 2 - 5 - 3 \cdot 3}{12} = 0$

Step 2.8.2

Subtract

$3 m$ from

$2 m$ .

$\frac{- m \cdot 2 - 5 - 3 \cdot 3}{12} = 0$

Step 2.8.3

Multiply

$2$ by

$- 1$ .

$\frac{- 2 m - 5 - 3 \cdot 3}{12} = 0$

Step 2.8.4

Multiply

$- 3$ by

$3$ .

$\frac{- 2 m - 5 - 9}{12} = 0$

Step 2.9

Subtract

$9$ from

$- 5$ .

$\frac{- 2 m - 14}{12} = 0$

Step 2.10

Cancel the common factor of

$- 2 m - 14$ and

$12$ .

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Step 2.10.1

Factor

$2$ out of

$- 2 m$ .

$\frac{2 (- m) - 14}{12} = 0$

Step 2.10.2

Factor

$2$ out of

$- 14$ .

$\frac{2 (- m) + 2 (- 7)}{12} = 0$

Step 2.10.3

Factor

$2$ out of

$2 (- m) + 2 (- 7)$ .

$\frac{2 (- m - 7)}{12} = 0$

Step 2.10.4

Cancel the common factors.

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Step 2.10.4.1

Factor

$2$ out of

$12$ .

$\frac{2 (- m - 7)}{2 (6)} = 0$

Step 2.10.4.2

Cancel the common factor.

$\frac{2 (- m - 7)}{2 \cdot 6} = 0$

Step 2.10.4.3

Rewrite the expression.

$\frac{- m - 7}{6} = 0$

Step 2.11

Factor

$- 1$ out of

$- m$ .

$\frac{- (m) - 7}{6} = 0$

Step 2.12

Rewrite

$- 7$ as

$- 1 (7)$ .

$\frac{- (m) - 1 (7)}{6} = 0$

Step 2.13

Factor

$- 1$ out of

$- (m) - 1 (7)$ .

$\frac{- (m + 7)}{6} = 0$

Step 2.14

Rewrite

$- (m + 7)$ as

$- 1 (m + 7)$ .

$\frac{- 1 (m + 7)}{6} = 0$

Step 2.15

Move the negative in front of the fraction.

$- \frac{m + 7}{6} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.