Finite Math Examples

$\frac{x}{6} + \frac{1}{2} = \frac{1}{12}$

Step 1

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

Tap for more steps...

Step 1.1

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

$\frac{x}{6} = \frac{1}{12} - \frac{1}{2}$

Step 1.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{6} = \frac{1}{12} - \frac{1}{2} \cdot \frac{6}{6}$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{x}{6} = \frac{1}{12} - \frac{6}{2 \cdot 6}$

Step 1.3.2

Multiply $2$ by $6$ .

$\frac{x}{6} = \frac{1}{12} - \frac{6}{12}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x}{6} = \frac{1 - 6}{12}$

Step 1.5

Subtract $6$ from $1$ .

$\frac{x}{6} = \frac{- 5}{12}$

Step 1.6

Move the negative in front of the fraction.

$\frac{x}{6} = - \frac{5}{12}$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 (- \frac{5}{12})$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 (- \frac{5}{12})$

Step 3.1.1.2

Rewrite the expression.

$x = 6 (- \frac{5}{12})$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $6 (- \frac{5}{12})$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.2.1.1.1

Move the leading negative in $- \frac{5}{12}$ into the numerator.

$x = 6 (\frac{- 5}{12})$

Step 3.2.1.1.2

Factor $6$ out of $12$ .

$x = 6 \frac{- 5}{6 (2)}$

Step 3.2.1.1.3

Cancel the common factor.

$x = 6 \frac{- 5}{6 \cdot 2}$

Step 3.2.1.1.4

Rewrite the expression.

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

Step 3.2.1.2

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.5$

Mixed Number Form:

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