Finite Math Examples

$\frac{2 x + 1}{2} - \frac{3}{4} = \frac{7 x}{8}$

Step 1

Subtract $\frac{7 x}{8}$ from both sides of the equation.

$\frac{2 x + 1}{2} - \frac{3}{4} - \frac{7 x}{8} = 0$

Step 2

Simplify $\frac{2 x + 1}{2} - \frac{3}{4} - \frac{7 x}{8}$ .

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Step 2.1

To write $\frac{2 x + 1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x + 1}{2} \cdot \frac{2}{2} - \frac{3}{4} - \frac{7 x}{8} = 0$

Step 2.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{2 x + 1}{2}$ by $\frac{2}{2}$ .

$\frac{(2 x + 1) \cdot 2}{2 \cdot 2} - \frac{3}{4} - \frac{7 x}{8} = 0$

Step 2.2.2

Multiply $2$ by $2$ .

$\frac{(2 x + 1) \cdot 2}{4} - \frac{3}{4} - \frac{7 x}{8} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{(2 x + 1) \cdot 2 - 3}{4} - \frac{7 x}{8} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Apply the distributive property.

$\frac{2 x \cdot 2 + 1 \cdot 2 - 3}{4} - \frac{7 x}{8} = 0$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{4 x + 1 \cdot 2 - 3}{4} - \frac{7 x}{8} = 0$

Step 2.4.3

Multiply $2$ by $1$ .

$\frac{4 x + 2 - 3}{4} - \frac{7 x}{8} = 0$

Step 2.4.4

Subtract $3$ from $2$ .

$\frac{4 x - 1}{4} - \frac{7 x}{8} = 0$

Step 2.5

To write $\frac{4 x - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x - 1}{4} \cdot \frac{2}{2} - \frac{7 x}{8} = 0$

Step 2.6

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.6.1

Multiply $\frac{4 x - 1}{4}$ by $\frac{2}{2}$ .

$\frac{(4 x - 1) \cdot 2}{4 \cdot 2} - \frac{7 x}{8} = 0$

Step 2.6.2

Multiply $4$ by $2$ .

$\frac{(4 x - 1) \cdot 2}{8} - \frac{7 x}{8} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{(4 x - 1) \cdot 2 - 7 x}{8} = 0$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Apply the distributive property.

$\frac{4 x \cdot 2 - 1 \cdot 2 - 7 x}{8} = 0$

Step 2.8.2

Multiply $2$ by $4$ .

$\frac{8 x - 1 \cdot 2 - 7 x}{8} = 0$

Step 2.8.3

Multiply $- 1$ by $2$ .

$\frac{8 x - 2 - 7 x}{8} = 0$

Step 2.8.4

Subtract $7 x$ from $8 x$ .

$\frac{x - 2}{8} = 0$

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.