Finite Math Examples

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

Step 1

Simplify the right side.

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Step 1.1

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.2

Add $5$ and $\frac{1}{2}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $5$ by $2$ .

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

Step 1.1.2.4.2

Add $10$ and $1$ .

$x - 3 = - \frac{11}{2}$

Step 2

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

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Step 2.1

Add $3$ to both sides of the equation.

$x = - \frac{11}{2} + 3$

Step 2.2

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

$x = - \frac{11}{2} + 3 \cdot \frac{2}{2}$

Step 2.3

Combine $3$ and $\frac{2}{2}$ .

$x = - \frac{11}{2} + \frac{3 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$x = \frac{- 11 + 3 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $2$ .

$x = \frac{- 11 + 6}{2}$

Step 2.5.2

Add $- 11$ and $6$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.5$

Mixed Number Form:

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