Finite Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $4$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Subtract $4$ from $1$ .

$\frac{x}{4} = \frac{- 3}{8}$

Step 1.6

Move the negative in front of the fraction.

$\frac{x}{4} = - \frac{3}{8}$

Step 2

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (- \frac{3}{8})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 (- \frac{3}{8})$

Step 3.1.1.2

Rewrite the expression.

$x = 4 (- \frac{3}{8})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $4 (- \frac{3}{8})$ .

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Step 3.2.1.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$x = 4 (\frac{- 3}{8})$

Step 3.2.1.1.2

Factor $4$ out of $8$ .

$x = 4 \frac{- 3}{4 (2)}$

Step 3.2.1.1.3

Cancel the common factor.

$x = 4 \frac{- 3}{4 \cdot 2}$

Step 3.2.1.1.4

Rewrite the expression.

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

Step 3.2.1.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.5$

Mixed Number Form:

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