Finite Math Examples

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

Step 1

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

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Step 1.1

Combine $\frac{1}{2}$ and $X$ .

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

Step 1.2

Add $X$ and $2 X$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Find the common denominator.

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Step 1.6.1

Write $- 12$ as a fraction with denominator $1$ .

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

Step 1.6.2

Multiply $\frac{- 12}{1}$ by $\frac{2}{2}$ .

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

Step 1.6.3

Multiply $\frac{- 12}{1}$ by $\frac{2}{2}$ .

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

Step 1.6.4

Write $- 171$ as a fraction with denominator $1$ .

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

Step 1.6.5

Multiply $\frac{- 171}{1}$ by $\frac{2}{2}$ .

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

Step 1.6.6

Multiply $\frac{- 171}{1}$ by $\frac{2}{2}$ .

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

Step 1.6.7

Write $6$ as a fraction with denominator $1$ .

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

Step 1.6.8

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

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

Step 1.6.9

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

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

Step 1.7

Combine the numerators over the common denominator.

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

Step 1.8

Simplify each term.

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Step 1.8.1

Multiply $2$ by $3$ .

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

Step 1.8.2

Multiply $- 12$ by $2$ .

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

Step 1.8.3

Multiply $- 171$ by $2$ .

$\frac{6 X + X - 24 - 342 + 6 \cdot 2}{2} = 180$

Step 1.8.4

Multiply $6$ by $2$ .

$\frac{6 X + X - 24 - 342 + 12}{2} = 180$

Step 1.9

Simplify by adding terms.

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Step 1.9.1

Add $6 X$ and $X$ .

$\frac{7 X - 24 - 342 + 12}{2} = 180$

Step 1.9.2

Simplify by adding and subtracting.

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Step 1.9.2.1

Subtract $342$ from $- 24$ .

$\frac{7 X - 366 + 12}{2} = 180$

Step 1.9.2.2

Add $- 366$ and $12$ .

$\frac{7 X - 354}{2} = 180$

Step 2

Multiply both sides by $2$ .

$\frac{7 X - 354}{2} \cdot 2 = 180 \cdot 2$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{7 X - 354}{2} \cdot 2 = 180 \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$7 X - 354 = 180 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $180$ by $2$ .

$7 X - 354 = 360$

Step 4

Solve for $X$ .

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Step 4.1

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

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Step 4.1.1

Add $354$ to both sides of the equation.

$7 X = 360 + 354$

Step 4.1.2

Add $360$ and $354$ .

$7 X = 714$

Step 4.2

Divide each term in $7 X = 714$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 X = 714$ by $7$ .

$\frac{7 X}{7} = \frac{714}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 X}{7} = \frac{714}{7}$

Step 4.2.2.1.2

Divide $X$ by $1$ .

$X = \frac{714}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $714$ by $7$ .

$X = 102$