Algebra Examples

$- 6 q = - 18 (\frac{2}{3} q + 2 - \frac{1}{6} q)$

Step 1

Since $q$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 18 (\frac{2}{3} q + 2 - \frac{1}{6} q) = - 6 q$

Step 2

Simplify $- 18 (\frac{2}{3} q + 2 - \frac{1}{6} q)$ .

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Step 2.1

Rewrite.

$0 + 0 - 18 (\frac{2}{3} q + 2 - \frac{1}{6} q) = - 6 q$

Step 2.2

Simplify by adding zeros.

$- 18 (\frac{2}{3} q + 2 - \frac{1}{6} q) = - 6 q$

Step 2.3

Simplify each term.

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Step 2.3.1

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

$- 18 (\frac{2 q}{3} + 2 - \frac{1}{6} q) = - 6 q$

Step 2.3.2

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

$- 18 (\frac{2 q}{3} + 2 - \frac{q}{6}) = - 6 q$

Step 2.4

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

$- 18 (\frac{2 q}{3} \cdot \frac{2}{2} - \frac{q}{6} + 2) = - 6 q$

Step 2.5

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

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Step 2.5.1

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

$- 18 (\frac{2 q \cdot 2}{3 \cdot 2} - \frac{q}{6} + 2) = - 6 q$

Step 2.5.2

Multiply $3$ by $2$ .

$- 18 (\frac{2 q \cdot 2}{6} - \frac{q}{6} + 2) = - 6 q$

Step 2.6

Combine the numerators over the common denominator.

$- 18 (\frac{2 q \cdot 2 - q}{6} + 2) = - 6 q$

Step 2.7

Simplify each term.

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Step 2.7.1

Simplify the numerator.

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Step 2.7.1.1

Factor $q$ out of $2 q \cdot 2 - q$ .

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Step 2.7.1.1.1

Factor $q$ out of $2 q \cdot 2$ .

$- 18 (\frac{q (2 \cdot 2) - q}{6} + 2) = - 6 q$

Step 2.7.1.1.2

Factor $q$ out of $- q$ .

$- 18 (\frac{q (2 \cdot 2) + q \cdot - 1}{6} + 2) = - 6 q$

Step 2.7.1.1.3

Factor $q$ out of $q (2 \cdot 2) + q \cdot - 1$ .

$- 18 (\frac{q (2 \cdot 2 - 1)}{6} + 2) = - 6 q$

Step 2.7.1.2

Multiply $2$ by $2$ .

$- 18 (\frac{q (4 - 1)}{6} + 2) = - 6 q$

Step 2.7.1.3

Subtract $1$ from $4$ .

$- 18 (\frac{q \cdot 3}{6} + 2) = - 6 q$

Step 2.7.2

Cancel the common factor of $3$ and $6$ .

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Step 2.7.2.1

Factor $3$ out of $q \cdot 3$ .

$- 18 (\frac{3 \cdot q}{6} + 2) = - 6 q$

Step 2.7.2.2

Cancel the common factors.

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Step 2.7.2.2.1

Factor $3$ out of $6$ .

$- 18 (\frac{3 \cdot q}{3 \cdot 2} + 2) = - 6 q$

Step 2.7.2.2.2

Cancel the common factor.

$- 18 (\frac{3 \cdot q}{3 \cdot 2} + 2) = - 6 q$

Step 2.7.2.2.3

Rewrite the expression.

$- 18 (\frac{q}{2} + 2) = - 6 q$

Step 2.8

Simplify terms.

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Step 2.8.1

Apply the distributive property.

$- 18 \frac{q}{2} - 18 \cdot 2 = - 6 q$

Step 2.8.2

Cancel the common factor of $2$ .

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Step 2.8.2.1

Factor $2$ out of $- 18$ .

$2 (- 9) \frac{q}{2} - 18 \cdot 2 = - 6 q$

Step 2.8.2.2

Cancel the common factor.

$2 \cdot - 9 \frac{q}{2} - 18 \cdot 2 = - 6 q$

Step 2.8.2.3

Rewrite the expression.

$- 9 q - 18 \cdot 2 = - 6 q$

Step 2.8.3

Multiply $- 18$ by $2$ .

$- 9 q - 36 = - 6 q$

Step 3

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

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Step 3.1

Add $6 q$ to both sides of the equation.

$- 9 q - 36 + 6 q = 0$

Step 3.2

Add $- 9 q$ and $6 q$ .

$- 3 q - 36 = 0$

Step 4

Add $36$ to both sides of the equation.

$- 3 q = 36$

Step 5

Divide each term in $- 3 q = 36$ by $- 3$ and simplify.

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Step 5.1

Divide each term in $- 3 q = 36$ by $- 3$ .

$\frac{- 3 q}{- 3} = \frac{36}{- 3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 3 q}{- 3} = \frac{36}{- 3}$

Step 5.2.1.2

Divide $q$ by $1$ .

$q = \frac{36}{- 3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $36$ by $- 3$ .

$q = - 12$