Pre-Algebra Examples

$\frac{3}{8} x - \frac{1}{12} = \frac{5}{6} - x$

Step 1

Combine $\frac{3}{8}$ and $x$ .

$\frac{3 x}{8} - \frac{1}{12} = \frac{5}{6} - x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Add $x$ to both sides of the equation.

$\frac{3 x}{8} - \frac{1}{12} + x = \frac{5}{6}$

Step 2.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3 x}{8} + x \cdot \frac{8}{8} - \frac{1}{12} = \frac{5}{6}$

Step 2.3

Combine $x$ and $\frac{8}{8}$ .

$\frac{3 x}{8} + \frac{x \cdot 8}{8} - \frac{1}{12} = \frac{5}{6}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x + x \cdot 8}{8} - \frac{1}{12} = \frac{5}{6}$

Step 2.5

Add $3 x$ and $x \cdot 8$ .

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Step 2.5.1

Reorder $x$ and $8$ .

$\frac{3 x + 8 \cdot x}{8} - \frac{1}{12} = \frac{5}{6}$

Step 2.5.2

Add $3 x$ and $8 \cdot x$ .

$\frac{11 x}{8} - \frac{1}{12} = \frac{5}{6}$

Step 3

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

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Step 3.1

Add $\frac{1}{12}$ to both sides of the equation.

$\frac{11 x}{8} = \frac{5}{6} + \frac{1}{12}$

Step 3.2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 x}{8} = \frac{5}{6} \cdot \frac{2}{2} + \frac{1}{12}$

Step 3.3

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

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Step 3.3.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{11 x}{8} = \frac{5 \cdot 2}{6 \cdot 2} + \frac{1}{12}$

Step 3.3.2

Multiply $6$ by $2$ .

$\frac{11 x}{8} = \frac{5 \cdot 2}{12} + \frac{1}{12}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{11 x}{8} = \frac{5 \cdot 2 + 1}{12}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $5$ by $2$ .

$\frac{11 x}{8} = \frac{10 + 1}{12}$

Step 3.5.2

Add $10$ and $1$ .

$\frac{11 x}{8} = \frac{11}{12}$

Step 4

Multiply both sides of the equation by $\frac{8}{11}$ .

$\frac{8}{11} \cdot \frac{11 x}{8} = \frac{8}{11} \cdot \frac{11}{12}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{8}{11} \cdot \frac{11 x}{8}$ .

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Step 5.1.1.1

Cancel the common factor of $8$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{8}{11} \cdot \frac{11 x}{8} = \frac{8}{11} \cdot \frac{11}{12}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{8}{11} \cdot \frac{11}{12}$

Step 5.1.1.2

Cancel the common factor of $11$ .

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Step 5.1.1.2.1

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{8}{11} \cdot \frac{11}{12}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{8}{11} \cdot \frac{11}{12}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{8}{11} \cdot \frac{11}{12}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{8}{11} \cdot \frac{11}{12}$ .

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Step 5.2.1.1

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Factor $4$ out of $8$ .

$x = \frac{4 (2)}{11} \cdot \frac{11}{12}$

Step 5.2.1.1.2

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 2}{11} \cdot \frac{11}{4 \cdot 3}$

Step 5.2.1.1.3

Cancel the common factor.

$x = \frac{4 \cdot 2}{11} \cdot \frac{11}{4 \cdot 3}$

Step 5.2.1.1.4

Rewrite the expression.

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

Step 5.2.1.2

Cancel the common factor of $11$ .

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Step 5.2.1.2.1

Cancel the common factor.

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

Step 5.2.1.2.2

Rewrite the expression.

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

Step 5.2.1.3

Combine $2$ and $\frac{1}{3}$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$