Basic Math Examples

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

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

Step 1

Rewrite the equation as

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

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

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

$q$ and

\frac{7}{4}

$\frac{7}{4}$ .

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

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

Step 2.2

Move

7

$7$ to the left of

q

$q$ .

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

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

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

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

Step 3

Move all terms not containing

q

$q$ to the right side of the equation.

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Step 3.1

Subtract

480

$480$ from both sides of the equation.

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

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

Step 3.2

Subtract

480

$480$ from

333

$333$ .

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

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

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

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

Step 4

Multiply both sides of the equation by

- \frac{4}{7}

$- \frac{4}{7}$ .

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

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

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})

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

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Step 5.1.1.1

Cancel the common factor of

4

$4$ .

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Step 5.1.1.1.1

Move the leading negative in

- \frac{4}{7}

$- \frac{4}{7}$ into the numerator.

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

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

Step 5.1.1.1.2

Move the leading negative in

- \frac{7 q}{4}

$- \frac{7 q}{4}$ into the numerator.

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

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

Step 5.1.1.1.3

Factor

4

$4$ out of

- 4

$- 4$ .

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

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

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

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

Step 5.1.1.1.5

Rewrite the expression.

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

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

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

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

Step 5.1.1.2

Cancel the common factor of

7

$7$ .

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Step 5.1.1.2.1

Factor

7

$7$ out of

- 7 q

$- 7 q$ .

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

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

Step 5.1.1.2.2

Cancel the common factor.

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

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

Step 5.1.1.2.3

Rewrite the expression.

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

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

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

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

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

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

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

Step 5.1.1.3.2

Multiply

q

$q$ by

1

$1$ .

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

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

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

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

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

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

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

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

- \frac{4}{7} \cdot - 147

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

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Step 5.2.1.1

Cancel the common factor of

7

$7$ .

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Step 5.2.1.1.1

Move the leading negative in

- \frac{4}{7}

$- \frac{4}{7}$ into the numerator.

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

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

Step 5.2.1.1.2

Factor

7

$7$ out of

- 147

$- 147$ .

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

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

Step 5.2.1.1.3

Cancel the common factor.

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

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

Step 5.2.1.1.4

Rewrite the expression.

q = - 4 \cdot - 21

$q = - 4 \cdot - 21$

q = - 4 \cdot - 21

$q = - 4 \cdot - 21$

Step 5.2.1.2

Multiply

- 4

$- 4$ by

- 21

$- 21$ .

q = 84

$q = 84$

q = 84

$q = 84$

q = 84

$q = 84$

q = 84

$q = 84$