Finite Math Examples

$(X + 2 X + \frac{1}{2}) + (- 12 - 171 + 6) = 180$

Step 1

Simplify $X + 2 X + \frac{1}{2} - 12 - 171 + 6$ .

Tap for more steps...

Step 1.1

Add $X$ and $2 X$ .

$3 X + \frac{1}{2} - 12 - 171 + 6 = 180$

Step 1.2

To write $- 12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 X + \frac{1}{2} - 12 \cdot \frac{2}{2} - 171 + 6 = 180$

Step 1.3

Combine $- 12$ and $\frac{2}{2}$ .

$3 X + \frac{1}{2} + \frac{- 12 \cdot 2}{2} - 171 + 6 = 180$

Step 1.4

Combine the numerators over the common denominator.

$3 X + \frac{1 - 12 \cdot 2}{2} - 171 + 6 = 180$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $- 12$ by $2$ .

$3 X + \frac{1 - 24}{2} - 171 + 6 = 180$

Step 1.5.2

Subtract $24$ from $1$ .

$3 X + \frac{- 23}{2} - 171 + 6 = 180$

Step 1.6

Move the negative in front of the fraction.

$3 X - \frac{23}{2} - 171 + 6 = 180$

Step 1.7

To write $- 171$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 X - \frac{23}{2} - 171 \cdot \frac{2}{2} + 6 = 180$

Step 1.8

Combine $- 171$ and $\frac{2}{2}$ .

$3 X - \frac{23}{2} + \frac{- 171 \cdot 2}{2} + 6 = 180$

Step 1.9

Combine the numerators over the common denominator.

$3 X + \frac{- 23 - 171 \cdot 2}{2} + 6 = 180$

Step 1.10

Simplify the numerator.

Tap for more steps...

Step 1.10.1

Multiply $- 171$ by $2$ .

$3 X + \frac{- 23 - 342}{2} + 6 = 180$

Step 1.10.2

Subtract $342$ from $- 23$ .

$3 X + \frac{- 365}{2} + 6 = 180$

Step 1.11

Move the negative in front of the fraction.

$3 X - \frac{365}{2} + 6 = 180$

Step 1.12

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

$3 X - \frac{365}{2} + 6 \cdot \frac{2}{2} = 180$

Step 1.13

Combine $6$ and $\frac{2}{2}$ .

$3 X - \frac{365}{2} + \frac{6 \cdot 2}{2} = 180$

Step 1.14

Combine the numerators over the common denominator.

$3 X + \frac{- 365 + 6 \cdot 2}{2} = 180$

Step 1.15

Simplify the numerator.

Tap for more steps...

Step 1.15.1

Multiply $6$ by $2$ .

$3 X + \frac{- 365 + 12}{2} = 180$

Step 1.15.2

Add $- 365$ and $12$ .

$3 X + \frac{- 353}{2} = 180$

Step 1.16

Move the negative in front of the fraction.

$3 X - \frac{353}{2} = 180$

Step 2

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

Tap for more steps...

Step 2.1

Add $\frac{353}{2}$ to both sides of the equation.

$3 X = 180 + \frac{353}{2}$

Step 2.2

To write $180$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 X = 180 \cdot \frac{2}{2} + \frac{353}{2}$

Step 2.3

Combine $180$ and $\frac{2}{2}$ .

$3 X = \frac{180 \cdot 2}{2} + \frac{353}{2}$

Step 2.4

Combine the numerators over the common denominator.

$3 X = \frac{180 \cdot 2 + 353}{2}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $180$ by $2$ .

$3 X = \frac{360 + 353}{2}$

Step 2.5.2

Add $360$ and $353$ .

$3 X = \frac{713}{2}$

Step 3

Divide each term in $3 X = \frac{713}{2}$ by $3$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $3 X = \frac{713}{2}$ by $3$ .

$\frac{3 X}{3} = \frac{\frac{713}{2}}{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{3 X}{3} = \frac{\frac{713}{2}}{3}$

Step 3.2.1.2

Divide $X$ by $1$ .

$X = \frac{\frac{713}{2}}{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$X = \frac{713}{2} \cdot \frac{1}{3}$

Step 3.3.2

Multiply $\frac{713}{2} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 3.3.2.1

Multiply $\frac{713}{2}$ by $\frac{1}{3}$ .

$X = \frac{713}{2 \cdot 3}$

Step 3.3.2.2

Multiply $2$ by $3$ .

$X = \frac{713}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$X = \frac{713}{6}$

Decimal Form:

$X = 118.8\overline{3}$

Mixed Number Form:

$X = 118 \frac{5}{6}$