Pre-Algebra Examples

$\frac{x + 1}{6} - \frac{x + 3}{4} = - 1$

Step 1

Simplify $\frac{x + 1}{6} - \frac{x + 3}{4}$ .

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Step 1.1

To write $\frac{x + 1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x + 1}{6} \cdot \frac{2}{2} - \frac{x + 3}{4} = - 1$

Step 1.2

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

$\frac{x + 1}{6} \cdot \frac{2}{2} - \frac{x + 3}{4} \cdot \frac{3}{3} = - 1$

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 $\frac{x + 1}{6}$ by $\frac{2}{2}$ .

$\frac{(x + 1) \cdot 2}{6 \cdot 2} - \frac{x + 3}{4} \cdot \frac{3}{3} = - 1$

Step 1.3.2

Multiply $6$ by $2$ .

$\frac{(x + 1) \cdot 2}{12} - \frac{x + 3}{4} \cdot \frac{3}{3} = - 1$

Step 1.3.3

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

$\frac{(x + 1) \cdot 2}{12} - \frac{(x + 3) \cdot 3}{4 \cdot 3} = - 1$

Step 1.3.4

Multiply $4$ by $3$ .

$\frac{(x + 1) \cdot 2}{12} - \frac{(x + 3) \cdot 3}{12} = - 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(x + 1) \cdot 2 - (x + 3) \cdot 3}{12} = - 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

$\frac{x \cdot 2 + 1 \cdot 2 - (x + 3) \cdot 3}{12} = - 1$

Step 1.5.2

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

$\frac{2 \cdot x + 1 \cdot 2 - (x + 3) \cdot 3}{12} = - 1$

Step 1.5.3

Multiply $2$ by $1$ .

$\frac{2 \cdot x + 2 - (x + 3) \cdot 3}{12} = - 1$

Step 1.5.4

Apply the distributive property.

$\frac{2 x + 2 + (- x - 1 \cdot 3) \cdot 3}{12} = - 1$

Step 1.5.5

Multiply $- 1$ by $3$ .

$\frac{2 x + 2 + (- x - 3) \cdot 3}{12} = - 1$

Step 1.5.6

Apply the distributive property.

$\frac{2 x + 2 - x \cdot 3 - 3 \cdot 3}{12} = - 1$

Step 1.5.7

Multiply $3$ by $- 1$ .

$\frac{2 x + 2 - 3 x - 3 \cdot 3}{12} = - 1$

Step 1.5.8

Multiply $- 3$ by $3$ .

$\frac{2 x + 2 - 3 x - 9}{12} = - 1$

Step 1.5.9

Subtract $3 x$ from $2 x$ .

$\frac{- x + 2 - 9}{12} = - 1$

Step 1.5.10

Subtract $9$ from $2$ .

$\frac{- x - 7}{12} = - 1$

Step 1.6

Simplify with factoring out.

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Step 1.6.1

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 7}{12} = - 1$

Step 1.6.2

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{- (x) - 1 (7)}{12} = - 1$

Step 1.6.3

Factor $- 1$ out of $- (x) - 1 (7)$ .

$\frac{- (x + 7)}{12} = - 1$

Step 1.6.4

Simplify the expression.

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Step 1.6.4.1

Rewrite $- (x + 7)$ as $- 1 (x + 7)$ .

$\frac{- 1 (x + 7)}{12} = - 1$

Step 1.6.4.2

Move the negative in front of the fraction.

$- \frac{x + 7}{12} = - 1$

Step 2

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{x + 7}{12}) = - 12 \cdot - 1$

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

Simplify $- 12 (- \frac{x + 7}{12})$ .

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Step 3.1.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{x + 7}{12}$ into the numerator.

$- 12 \frac{- (x + 7)}{12} = - 12 \cdot - 1$

Step 3.1.1.1.2

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- (x + 7)}{12} = - 12 \cdot - 1$

Step 3.1.1.1.3

Cancel the common factor.

$12 \cdot - 1 \frac{- (x + 7)}{12} = - 12 \cdot - 1$

Step 3.1.1.1.4

Rewrite the expression.

$- - (x + 7) = - 12 \cdot - 1$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (x + 7) = - 12 \cdot - 1$

Step 3.1.1.2.2

Multiply $x + 7$ by $1$ .

$x + 7 = - 12 \cdot - 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 12$ by $- 1$ .

$x + 7 = 12$

Step 4

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

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Step 4.1

Subtract $7$ from both sides of the equation.

$x = 12 - 7$

Step 4.2

Subtract $7$ from $12$ .

$x = 5$