Finite Math Examples

$\frac{3 x}{5} = \frac{x}{2} - \frac{1}{5}$

Step 1

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

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Step 1.1

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{3 x}{5} - \frac{x}{2} = - \frac{1}{5}$

Step 1.2

Add $\frac{1}{5}$ to both sides of the equation.

$\frac{3 x}{5} - \frac{x}{2} + \frac{1}{5} = 0$

Step 2

Simplify $\frac{3 x}{5} - \frac{x}{2} + \frac{1}{5}$ .

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Step 2.1

To write $\frac{3 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{5} \cdot \frac{2}{2} - \frac{x}{2} + \frac{1}{5} = 0$

Step 2.2

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

$\frac{3 x}{5} \cdot \frac{2}{2} - \frac{x}{2} \cdot \frac{5}{5} + \frac{1}{5} = 0$

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 $\frac{3 x}{5}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2}{5 \cdot 2} - \frac{x}{2} \cdot \frac{5}{5} + \frac{1}{5} = 0$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{3 x \cdot 2}{10} - \frac{x}{2} \cdot \frac{5}{5} + \frac{1}{5} = 0$

Step 2.3.3

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

$\frac{3 x \cdot 2}{10} - \frac{x \cdot 5}{2 \cdot 5} + \frac{1}{5} = 0$

Step 2.3.4

Multiply $2$ by $5$ .

$\frac{3 x \cdot 2}{10} - \frac{x \cdot 5}{10} + \frac{1}{5} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 - x \cdot 5}{10} + \frac{1}{5} = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $3 x \cdot 2 - x \cdot 5$ .

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Step 2.5.1.1.1

Factor $x$ out of $3 x \cdot 2$ .

$\frac{x (3 \cdot 2) - x \cdot 5}{10} + \frac{1}{5} = 0$

Step 2.5.1.1.2

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (3 \cdot 2) + x (- 1 \cdot 5)}{10} + \frac{1}{5} = 0$

Step 2.5.1.1.3

Factor $x$ out of $x (3 \cdot 2) + x (- 1 \cdot 5)$ .

$\frac{x (3 \cdot 2 - 1 \cdot 5)}{10} + \frac{1}{5} = 0$

Step 2.5.1.2

Multiply $3$ by $2$ .

$\frac{x (6 - 1 \cdot 5)}{10} + \frac{1}{5} = 0$

Step 2.5.1.3

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{10} + \frac{1}{5} = 0$

Step 2.5.1.4

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{10} + \frac{1}{5} = 0$

Step 2.5.2

Multiply $x$ by $1$ .

$\frac{x}{10} + \frac{1}{5} = 0$

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.