Finite Math Examples

$(\frac{m + 2}{4}) + 5 = (\frac{2 m - 3}{3})$

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{m + 2}{4} + 5) \cdot 3$ .

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Step 2.1.1.1

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

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

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

Combine the numerators over the common denominator.

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

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Multiply $5$ by $4$ .

$\frac{m + 2 + 20}{4} \cdot 3 = \frac{2 m - 3}{3} \cdot 3$

Step 2.1.1.3.2

Add $2$ and $20$ .

$\frac{m + 22}{4} \cdot 3 = \frac{2 m - 3}{3} \cdot 3$

Step 2.1.1.4

Combine fractions.

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Step 2.1.1.4.1

Combine $\frac{m + 22}{4}$ and $3$ .

$\frac{(m + 22) \cdot 3}{4} = \frac{2 m - 3}{3} \cdot 3$

Step 2.1.1.4.2

Move $3$ to the left of $m + 22$ .

$\frac{3 (m + 22)}{4} = \frac{2 m - 3}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 (m + 22)}{4} = \frac{2 m - 3}{3} \cdot 3$

Step 2.2.1.2

Rewrite the expression.

$\frac{3 (m + 22)}{4} = 2 m - 3$

Step 3

Solve for $m$ .

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Step 3.1

Multiply both sides by $4$ .

$\frac{3 (m + 22)}{4} \cdot 4 = (2 m - 3) \cdot 4$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{3 (m + 22)}{4} \cdot 4$ .

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Step 3.2.1.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{3 (m + 22)}{4} \cdot 4 = (2 m - 3) \cdot 4$

Step 3.2.1.1.1.2

Rewrite the expression.

$3 (m + 22) = (2 m - 3) \cdot 4$

Step 3.2.1.1.2

Apply the distributive property.

$3 m + 3 \cdot 22 = (2 m - 3) \cdot 4$

Step 3.2.1.1.3

Multiply $3$ by $22$ .

$3 m + 66 = (2 m - 3) \cdot 4$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(2 m - 3) \cdot 4$ .

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Step 3.2.2.1.1

Apply the distributive property.

$3 m + 66 = 2 m \cdot 4 - 3 \cdot 4$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $4$ by $2$ .

$3 m + 66 = 8 m - 3 \cdot 4$

Step 3.2.2.1.2.2

Multiply $- 3$ by $4$ .

$3 m + 66 = 8 m - 12$

Step 3.3

Solve for $m$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $8 m$ from both sides of the equation.

$3 m + 66 - 8 m = - 12$

Step 3.3.1.2

Subtract $8 m$ from $3 m$ .

$- 5 m + 66 = - 12$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $66$ from both sides of the equation.

$- 5 m = - 12 - 66$

Step 3.3.2.2

Subtract $66$ from $- 12$ .

$- 5 m = - 78$

Step 3.3.3

Divide each term in $- 5 m = - 78$ by $- 5$ and simplify.

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Step 3.3.3.1

Divide each term in $- 5 m = - 78$ by $- 5$ .

$\frac{- 5 m}{- 5} = \frac{- 78}{- 5}$

Step 3.3.3.2

Simplify the left side.

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Step 3.3.3.2.1

Cancel the common factor of $- 5$ .

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Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 5 m}{- 5} = \frac{- 78}{- 5}$

Step 3.3.3.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 78}{- 5}$

Step 3.3.3.3

Simplify the right side.

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Step 3.3.3.3.1

Dividing two negative values results in a positive value.

$m = \frac{78}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = \frac{78}{5}$

Decimal Form:

$m = 15.6$

Mixed Number Form:

$m = 15 \frac{3}{5}$