Pre-Algebra Examples

$x + \frac{12}{8} = \frac{1}{4} x$

Step 1

Cancel the common factor of $12$ and $8$ .

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Step 1.1

Factor $4$ out of $12$ .

$x + \frac{4 (3)}{8} = \frac{1}{4} x$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $8$ .

$x + \frac{4 \cdot 3}{4 \cdot 2} = \frac{1}{4} x$

Step 1.2.2

Cancel the common factor.

$x + \frac{4 \cdot 3}{4 \cdot 2} = \frac{1}{4} x$

Step 1.2.3

Rewrite the expression.

$x + \frac{3}{2} = \frac{1}{4} x$

Step 2

Combine $\frac{1}{4}$ and $x$ .

$x + \frac{3}{2} = \frac{x}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{x}{4}$ from both sides of the equation.

$x + \frac{3}{2} - \frac{x}{4} = 0$

Step 3.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x \cdot \frac{4}{4} - \frac{x}{4} + \frac{3}{2} = 0$

Step 3.3

Combine $x$ and $\frac{4}{4}$ .

$\frac{x \cdot 4}{4} - \frac{x}{4} + \frac{3}{2} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x}{4} + \frac{3}{2} = 0$

Step 3.5

Subtract $x$ from $x \cdot 4$ .

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Step 3.5.1

Reorder $x$ and $4$ .

$\frac{4 \cdot x - x}{4} + \frac{3}{2} = 0$

Step 3.5.2

Subtract $x$ from $4 \cdot x$ .

$\frac{3 \cdot x}{4} + \frac{3}{2} = 0$

$\frac{3 x}{4} + \frac{3}{2} = 0$

Step 4

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{3 x}{4} = - \frac{3}{2}$

Step 5

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} (- \frac{3}{2})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} (- \frac{3}{2})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{4}{3} (- \frac{3}{2})$

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{4}{3} (- \frac{3}{2})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{4}{3} (- \frac{3}{2})$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{4}{3} (- \frac{3}{2})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{4}{3} (- \frac{3}{2})$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 6.2.1.1.2

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{3} \cdot \frac{- 3}{2}$

Step 6.2.1.1.3

Cancel the common factor.

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

Step 6.2.1.1.4

Rewrite the expression.

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

Step 6.2.1.2

Cancel the common factor of $3$ .

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Step 6.2.1.2.1

Factor $3$ out of $- 3$ .

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

Step 6.2.1.2.2

Cancel the common factor.

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

Step 6.2.1.2.3

Rewrite the expression.

$x = 2 \cdot - 1$

Step 6.2.1.3

Multiply $2$ by $- 1$ .

$x = - 2$