Finite Math Examples

$\frac{2}{5} q = 100 - \frac{2}{5} q$

Step 1

Simplify $\frac{2}{5} q$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{5} q = 100 - \frac{2}{5} q$

Step 1.2

Simplify by adding zeros.

$\frac{2}{5} q = 100 - \frac{2}{5} q$

Step 1.3

Combine $\frac{2}{5}$ and $q$ .

$\frac{2 q}{5} = 100 - \frac{2}{5} q$

Step 2

Simplify each term.

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Step 2.1

Combine $q$ and $\frac{2}{5}$ .

$\frac{2 q}{5} = 100 - \frac{q \cdot 2}{5}$

Step 2.2

Move $2$ to the left of $q$ .

$\frac{2 q}{5} = 100 - \frac{2 q}{5}$

Step 3

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

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Step 3.1

Add $\frac{2 q}{5}$ to both sides of the equation.

$\frac{2 q}{5} + \frac{2 q}{5} = 100$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 q + 2 q}{5} = 100$

Step 3.3

Add $2 q$ and $2 q$ .

$\frac{4 q}{5} = 100$

Step 4

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 q}{5} = \frac{5}{4} \cdot 100$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{4} \cdot \frac{4 q}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 q}{5} = \frac{5}{4} \cdot 100$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 q) = \frac{5}{4} \cdot 100$

Step 5.1.1.2

Cancel the common factor of $4$ .

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Step 5.1.1.2.1

Factor $4$ out of $4 q$ .

$\frac{1}{4} (4 (q)) = \frac{5}{4} \cdot 100$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 q) = \frac{5}{4} \cdot 100$

Step 5.1.1.2.3

Rewrite the expression.

$q = \frac{5}{4} \cdot 100$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{4} \cdot 100$ .

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Step 5.2.1.1

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Factor $4$ out of $100$ .

$q = \frac{5}{4} \cdot (4 (25))$

Step 5.2.1.1.2

Cancel the common factor.

$q = \frac{5}{4} \cdot (4 \cdot 25)$

Step 5.2.1.1.3

Rewrite the expression.

$q = 5 \cdot 25$

Step 5.2.1.2

Multiply $5$ by $25$ .

$q = 125$