Basic Math Examples

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

Step 1

Simplify $\frac{1}{6} x - \frac{1}{12} \cdot (x - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{6}$ and $x$ .

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Combine $x$ and $\frac{1}{12}$ .

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

Step 1.1.4

Multiply $- \frac{1}{12} \cdot - 1$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 1.1.4.2

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $6$ by $2$ .

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

Step 1.4

Simplify terms.

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Step 1.4.1

Combine the numerators over the common denominator.

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

Step 1.4.2

Combine the numerators over the common denominator.

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

Step 1.5

Move $2$ to the left of $x$ .

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

Step 1.6

Subtract $x$ from $2 x$ .

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

Step 2

Multiply both sides of the equation by $12$ .

$12 \frac{x + 1}{12} = 12 (\frac{1}{2})$

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 $12$ .

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Step 3.1.1.1

Cancel the common factor.

$12 \frac{x + 1}{12} = 12 (\frac{1}{2})$

Step 3.1.1.2

Rewrite the expression.

$x + 1 = 12 (\frac{1}{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $12$ .

$x + 1 = 2 (6) \frac{1}{2}$

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

$x + 1 = 6$

Step 4

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

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Step 4.1

Subtract $1$ from both sides of the equation.

$x = 6 - 1$

Step 4.2

Subtract $1$ from $6$ .

$x = 5$