Pre-Algebra Examples

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

Step 1

Multiply both sides of the equation by $6$ .

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

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $6 (\frac{1}{6} \cdot (\frac{2}{3} + x))$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Factor $2$ out of $6$ .

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

Step 2.1.1.2.2

Cancel the common factor.

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

Step 2.1.1.2.3

Rewrite the expression.

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

Step 2.1.1.3

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

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

Step 2.1.1.4

Multiply $3$ by $3$ .

$6 (\frac{1}{9} + \frac{1}{6} x) = 6 \cdot - 3$

Step 2.1.1.5

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

$6 (\frac{1}{9} + \frac{x}{6}) = 6 \cdot - 3$

Step 2.1.1.6

Apply the distributive property.

$6 (\frac{1}{9}) + 6 \frac{x}{6} = 6 \cdot - 3$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Factor $3$ out of $6$ .

$3 (2) \frac{1}{9} + 6 \frac{x}{6} = 6 \cdot - 3$

Step 2.1.1.7.2

Factor $3$ out of $9$ .

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

Step 2.1.1.7.3

Cancel the common factor.

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

Step 2.1.1.7.4

Rewrite the expression.

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

Step 2.1.1.8

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

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

Step 2.1.1.9

Cancel the common factor of $6$ .

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Step 2.1.1.9.1

Cancel the common factor.

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

Step 2.1.1.9.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $6$ by $- 3$ .

$\frac{2}{3} + x = - 18$

Step 3

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

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Step 3.1

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

$x = - 18 - \frac{2}{3}$

Step 3.2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - 18 \cdot \frac{3}{3} - \frac{2}{3}$

Step 3.3

Combine $- 18$ and $\frac{3}{3}$ .

$x = \frac{- 18 \cdot 3}{3} - \frac{2}{3}$

Step 3.4

Combine the numerators over the common denominator.

$x = \frac{- 18 \cdot 3 - 2}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 18$ by $3$ .

$x = \frac{- 54 - 2}{3}$

Step 3.5.2

Subtract $2$ from $- 54$ .

$x = \frac{- 56}{3}$

Step 3.6

Move the negative in front of the fraction.

$x = - \frac{56}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{56}{3}$

Decimal Form:

$x = - 18.\overline{6}$

Mixed Number Form:

$x = - 18 \frac{2}{3}$