Basic Math Examples

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(1 - \frac{2}{3} \cdot \frac{1}{2} \cdot (2 q)) \cdot 3$ .

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1.1.1

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

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

Step 2.1.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 2.1.1.1.1.3

Cancel the common factor.

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

Step 2.1.1.1.1.4

Rewrite the expression.

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

Step 2.1.1.1.2

Move the negative in front of the fraction.

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

Step 2.1.1.1.3

Multiply $- \frac{1}{3} (2 q)$ .

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Step 2.1.1.1.3.1

Multiply $2$ by $- 1$ .

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

Step 2.1.1.1.3.2

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

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

Step 2.1.1.1.3.3

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

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

Step 2.1.1.1.4

Move the negative in front of the fraction.

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

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Apply the distributive property.

$1 \cdot 3 - \frac{2 q}{3} \cdot 3 = - \frac{q}{3} \cdot 3$

Step 2.1.1.2.2

Multiply $3$ by $1$ .

$3 - \frac{2 q}{3} \cdot 3 = - \frac{q}{3} \cdot 3$

Step 2.1.1.2.3

Cancel the common factor of $3$ .

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Step 2.1.1.2.3.1

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

$3 + \frac{- 2 q}{3} \cdot 3 = - \frac{q}{3} \cdot 3$

Step 2.1.1.2.3.2

Cancel the common factor.

$3 + \frac{- 2 q}{3} \cdot 3 = - \frac{q}{3} \cdot 3$

Step 2.1.1.2.3.3

Rewrite the expression.

$3 - 2 q = - \frac{q}{3} \cdot 3$

Step 2.1.1.2.4

Reorder $3$ and $- 2 q$ .

$- 2 q + 3 = - \frac{q}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

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

$- 2 q + 3 = \frac{- q}{3} \cdot 3$

Step 2.2.1.2

Cancel the common factor.

$- 2 q + 3 = \frac{- q}{3} \cdot 3$

Step 2.2.1.3

Rewrite the expression.

$- 2 q + 3 = - q$

Step 3

Solve for $q$ .

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Step 3.1

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

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Step 3.1.1

Add $q$ to both sides of the equation.

$- 2 q + 3 + q = 0$

Step 3.1.2

Add $- 2 q$ and $q$ .

$- q + 3 = 0$

Step 3.2

Subtract $3$ from both sides of the equation.

$- q = - 3$

Step 3.3

Divide each term in $- q = - 3$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- q = - 3$ by $- 1$ .

$\frac{- q}{- 1} = \frac{- 3}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{q}{1} = \frac{- 3}{- 1}$

Step 3.3.2.2

Divide $q$ by $1$ .

$q = \frac{- 3}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 3$ by $- 1$ .

$q = 3$