Pre-Algebra Examples

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

Step 1

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

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

Step 2

Combine $\frac{3}{4}$ and $x$ .

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

Step 3

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

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Step 3.1

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$\frac{x}{3} - 4 - \frac{3 x}{4} = 1$

Step 3.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{3} \cdot \frac{4}{4} - \frac{3 x}{4} - 4 = 1$

Step 3.3

To write $- \frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{4}{4} - \frac{3 x}{4} \cdot \frac{3}{3} - 4 = 1$

Step 3.4

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

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Step 3.4.1

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{3 \cdot 4} - \frac{3 x}{4} \cdot \frac{3}{3} - 4 = 1$

Step 3.4.2

Multiply $3$ by $4$ .

$\frac{x \cdot 4}{12} - \frac{3 x}{4} \cdot \frac{3}{3} - 4 = 1$

Step 3.4.3

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{x \cdot 4}{12} - \frac{3 x \cdot 3}{4 \cdot 3} - 4 = 1$

Step 3.4.4

Multiply $4$ by $3$ .

$\frac{x \cdot 4}{12} - \frac{3 x \cdot 3}{12} - 4 = 1$

Step 3.5

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 3 x \cdot 3}{12} - 4 = 1$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $x$ out of $x \cdot 4 - 3 x \cdot 3$ .

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Step 3.6.1.1.1

Factor $x$ out of $x \cdot 4$ .

$\frac{x (4) - 3 x \cdot 3}{12} - 4 = 1$

Step 3.6.1.1.2

Factor $x$ out of $- 3 x \cdot 3$ .

$\frac{x (4) + x (- 3 \cdot 3)}{12} - 4 = 1$

Step 3.6.1.1.3

Factor $x$ out of $x (4) + x (- 3 \cdot 3)$ .

$\frac{x (4 - 3 \cdot 3)}{12} - 4 = 1$

Step 3.6.1.2

Multiply $- 3$ by $3$ .

$\frac{x (4 - 9)}{12} - 4 = 1$

Step 3.6.1.3

Subtract $9$ from $4$ .

$\frac{x \cdot - 5}{12} - 4 = 1$

Step 3.6.2

Move $- 5$ to the left of $x$ .

$\frac{- 5 \cdot x}{12} - 4 = 1$

Step 3.6.3

Move the negative in front of the fraction.

$- \frac{5 x}{12} - 4 = 1$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$- \frac{5 x}{12} = 1 + 4$

Step 4.2

Add $1$ and $4$ .

$- \frac{5 x}{12} = 5$

Step 5

Multiply both sides of the equation by $- \frac{12}{5}$ .

$- \frac{12}{5} (- \frac{5 x}{12}) = - \frac{12}{5} \cdot 5$

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 $- \frac{12}{5} (- \frac{5 x}{12})$ .

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Step 6.1.1.1

Cancel the common factor of $12$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{12}{5}$ into the numerator.

$\frac{- 12}{5} (- \frac{5 x}{12}) = - \frac{12}{5} \cdot 5$

Step 6.1.1.1.2

Move the leading negative in $- \frac{5 x}{12}$ into the numerator.

$\frac{- 12}{5} \cdot \frac{- 5 x}{12} = - \frac{12}{5} \cdot 5$

Step 6.1.1.1.3

Factor $12$ out of $- 12$ .

$\frac{12 (- 1)}{5} \cdot \frac{- 5 x}{12} = - \frac{12}{5} \cdot 5$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{12 \cdot - 1}{5} \cdot \frac{- 5 x}{12} = - \frac{12}{5} \cdot 5$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{12}{5} \cdot 5$

Step 6.1.1.2

Cancel the common factor of $5$ .

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Step 6.1.1.2.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) = - \frac{12}{5} \cdot 5$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{12}{5} \cdot 5$

Step 6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{12}{5} \cdot 5$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{12}{5} \cdot 5$

Step 6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{12}{5} \cdot 5$

Step 6.2

Simplify the right side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Move the leading negative in $- \frac{12}{5}$ into the numerator.

$x = \frac{- 12}{5} \cdot 5$

Step 6.2.1.2

Cancel the common factor.

$x = \frac{- 12}{5} \cdot 5$

Step 6.2.1.3

Rewrite the expression.

$x = - 12$