Basic Math Examples

$333 = 480 - \frac{7}{4} q$

Step 1

Rewrite the equation as $480 - \frac{7}{4} q = 333$ .

$480 - \frac{7}{4} q = 333$

Step 2

Simplify each term.

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Step 2.1

Combine $q$ and $\frac{7}{4}$ .

$480 - \frac{q \cdot 7}{4} = 333$

Step 2.2

Move $7$ to the left of $q$ .

$480 - \frac{7 q}{4} = 333$

Step 3

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

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Step 3.1

Subtract $480$ from both sides of the equation.

$- \frac{7 q}{4} = 333 - 480$

Step 3.2

Subtract $480$ from $333$ .

$- \frac{7 q}{4} = - 147$

Step 4

Multiply both sides of the equation by $- \frac{4}{7}$ .

$- \frac{4}{7} (- \frac{7 q}{4}) = - \frac{4}{7} \cdot - 147$

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 $- \frac{4}{7} (- \frac{7 q}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$\frac{- 4}{7} (- \frac{7 q}{4}) = - \frac{4}{7} \cdot - 147$

Step 5.1.1.1.2

Move the leading negative in $- \frac{7 q}{4}$ into the numerator.

$\frac{- 4}{7} \cdot \frac{- 7 q}{4} = - \frac{4}{7} \cdot - 147$

Step 5.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{7} \cdot \frac{- 7 q}{4} = - \frac{4}{7} \cdot - 147$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{7} \cdot \frac{- 7 q}{4} = - \frac{4}{7} \cdot - 147$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 q) = - \frac{4}{7} \cdot - 147$

Step 5.1.1.2

Cancel the common factor of $7$ .

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Step 5.1.1.2.1

Factor $7$ out of $- 7 q$ .

$\frac{- 1}{7} (7 (- q)) = - \frac{4}{7} \cdot - 147$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- q)) = - \frac{4}{7} \cdot - 147$

Step 5.1.1.2.3

Rewrite the expression.

$- - q = - \frac{4}{7} \cdot - 147$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 q = - \frac{4}{7} \cdot - 147$

Step 5.1.1.3.2

Multiply $q$ by $1$ .

$q = - \frac{4}{7} \cdot - 147$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{4}{7} \cdot - 147$ .

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Step 5.2.1.1

Cancel the common factor of $7$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$q = \frac{- 4}{7} \cdot - 147$

Step 5.2.1.1.2

Factor $7$ out of $- 147$ .

$q = \frac{- 4}{7} \cdot (7 (- 21))$

Step 5.2.1.1.3

Cancel the common factor.

$q = \frac{- 4}{7} \cdot (7 \cdot - 21)$

Step 5.2.1.1.4

Rewrite the expression.

$q = - 4 \cdot - 21$

Step 5.2.1.2

Multiply $- 4$ by $- 21$ .

$q = 84$