Pre-Algebra Examples

$- \frac{1}{6} \cdot (x - 12) + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1

Simplify $- \frac{1}{6} \cdot (x - 12) + \frac{1}{2} \cdot (x + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- \frac{1}{6} x - \frac{1}{6} \cdot - 12 + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.2

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

$- \frac{x}{6} - \frac{1}{6} \cdot - 12 + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.3

Cancel the common factor of $6$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$- \frac{x}{6} + \frac{- 1}{6} \cdot - 12 + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.3.2

Factor $6$ out of $- 12$ .

$- \frac{x}{6} + \frac{- 1}{6} \cdot (6 (- 2)) + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.3.3

Cancel the common factor.

$- \frac{x}{6} + \frac{- 1}{6} \cdot (6 \cdot - 2) + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.3.4

Rewrite the expression.

$- \frac{x}{6} - 1 \cdot - 2 + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.4

Multiply $- 1$ by $- 2$ .

$- \frac{x}{6} + 2 + \frac{1}{2} \cdot (x + 2) = x + 11$

Step 1.1.5

Apply the distributive property.

$- \frac{x}{6} + 2 + \frac{1}{2} x + \frac{1}{2} \cdot 2 = x + 11$

Step 1.1.6

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

$- \frac{x}{6} + 2 + \frac{x}{2} + \frac{1}{2} \cdot 2 = x + 11$

Step 1.1.7

Cancel the common factor of $2$ .

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Step 1.1.7.1

Cancel the common factor.

$- \frac{x}{6} + 2 + \frac{x}{2} + \frac{1}{2} \cdot 2 = x + 11$

Step 1.1.7.2

Rewrite the expression.

$- \frac{x}{6} + 2 + \frac{x}{2} + 1 = x + 11$

Step 1.2

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{6} + \frac{x}{2} \cdot \frac{3}{3} + 2 + 1 = x + 11$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{2}$ by $\frac{3}{3}$ .

$- \frac{x}{6} + \frac{x \cdot 3}{2 \cdot 3} + 2 + 1 = x + 11$

Step 1.3.2

Multiply $2$ by $3$ .

$- \frac{x}{6} + \frac{x \cdot 3}{6} + 2 + 1 = x + 11$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- x + x \cdot 3}{6} + 2 + 1 = x + 11$

Step 1.5

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

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Step 1.5.1

Reorder $x$ and $3$ .

$\frac{- x + 3 \cdot x}{6} + 2 + 1 = x + 11$

Step 1.5.2

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

$\frac{2 x}{6} + 2 + 1 = x + 11$

Step 1.6

Cancel the common factor of $2$ and $6$ .

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Step 1.6.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{6} + 2 + 1 = x + 11$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $6$ .

$\frac{2 x}{2 \cdot 3} + 2 + 1 = x + 11$

Step 1.6.2.2

Cancel the common factor.

$\frac{2 x}{2 \cdot 3} + 2 + 1 = x + 11$

Step 1.6.2.3

Rewrite the expression.

$\frac{x}{3} + 2 + 1 = x + 11$

Step 1.7

Add $2$ and $1$ .

$\frac{x}{3} + 3 = x + 11$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{x}{3} + 3 - x = 11$

Step 2.2

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

$\frac{x}{3} - x \cdot \frac{3}{3} + 3 = 11$

Step 2.3

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

$\frac{x}{3} + \frac{- x \cdot 3}{3} + 3 = 11$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 3}{3} + 3 = 11$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

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

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Step 2.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 3}{3} + 3 = 11$

Step 2.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 3}{3} + 3 = 11$

Step 2.5.1.1.3

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

$\frac{x \cdot 1 + x (- 1 \cdot 3)}{3} + 3 = 11$

Step 2.5.1.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 3)$ .

$\frac{x (1 - 1 \cdot 3)}{3} + 3 = 11$

Step 2.5.1.2

Multiply $- 1$ by $3$ .

$\frac{x (1 - 3)}{3} + 3 = 11$

Step 2.5.1.3

Subtract $3$ from $1$ .

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

Step 2.5.2

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

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

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{2 x}{3} + 3 = 11$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

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

Step 3.2

Subtract $3$ from $11$ .

$- \frac{2 x}{3} = 8$

Step 4

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 x}{3}) = - \frac{3}{2} \cdot 8$

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 $- \frac{3}{2} (- \frac{2 x}{3})$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

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

$\frac{- 3}{2} (- \frac{2 x}{3}) = - \frac{3}{2} \cdot 8$

Step 5.1.1.1.2

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

$\frac{- 3}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 8$

Step 5.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 8$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 x}{3} = - \frac{3}{2} \cdot 8$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{3}{2} \cdot 8$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{3}{2} \cdot 8$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{3}{2} \cdot 8$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{2} \cdot 8$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{2} \cdot 8$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{2} \cdot 8$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{3}{2} \cdot 8$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

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

$x = \frac{- 3}{2} \cdot 8$

Step 5.2.1.1.2

Factor $2$ out of $8$ .

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

Step 5.2.1.1.3

Cancel the common factor.

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

Step 5.2.1.1.4

Rewrite the expression.

$x = - 3 \cdot 4$

Step 5.2.1.2

Multiply $- 3$ by $4$ .

$x = - 12$