Basic Math Examples

$q = 160 - \frac{5}{2} p$

Step 1

Rewrite the equation as $160 - \frac{5}{2} p = q$ .

$160 - \frac{5}{2} p = q$

Step 2

Simplify each term.

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Step 2.1

Combine $p$ and $\frac{5}{2}$ .

$160 - \frac{p \cdot 5}{2} = q$

Step 2.2

Move $5$ to the left of $p$ .

$160 - \frac{5 p}{2} = q$

Step 3

Subtract $160$ from both sides of the equation.

$- \frac{5 p}{2} = q - 160$

Step 4

Multiply both sides of the equation by $- \frac{2}{5}$ .

$- \frac{2}{5} (- \frac{5 p}{2}) = - \frac{2}{5} (q - 160)$

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 $- \frac{2}{5} (- \frac{5 p}{2})$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} (- \frac{5 p}{2}) = - \frac{2}{5} (q - 160)$

Step 5.1.1.1.2

Move the leading negative in $- \frac{5 p}{2}$ into the numerator.

$\frac{- 2}{5} \cdot \frac{- 5 p}{2} = - \frac{2}{5} (q - 160)$

Step 5.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{5} \cdot \frac{- 5 p}{2} = - \frac{2}{5} (q - 160)$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{5} \cdot \frac{- 5 p}{2} = - \frac{2}{5} (q - 160)$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 p) = - \frac{2}{5} (q - 160)$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $- 5 p$ .

$\frac{- 1}{5} (5 (- p)) = - \frac{2}{5} (q - 160)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- p)) = - \frac{2}{5} (q - 160)$

Step 5.1.1.2.3

Rewrite the expression.

$- - p = - \frac{2}{5} (q - 160)$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{2}{5} (q - 160)$

Step 5.1.1.3.2

Multiply $p$ by $1$ .

$p = - \frac{2}{5} (q - 160)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{2}{5} (q - 160)$ .

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Step 5.2.1.1

Simplify terms.

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Step 5.2.1.1.1

Apply the distributive property.

$p = - \frac{2}{5} q - \frac{2}{5} \cdot - 160$

Step 5.2.1.1.2

Combine $q$ and $\frac{2}{5}$ .

$p = - \frac{q \cdot 2}{5} - \frac{2}{5} \cdot - 160$

Step 5.2.1.1.3

Cancel the common factor of $5$ .

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Step 5.2.1.1.3.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$p = - \frac{q \cdot 2}{5} + \frac{- 2}{5} \cdot - 160$

Step 5.2.1.1.3.2

Factor $5$ out of $- 160$ .

$p = - \frac{q \cdot 2}{5} + \frac{- 2}{5} \cdot (5 (- 32))$

Step 5.2.1.1.3.3

Cancel the common factor.

$p = - \frac{q \cdot 2}{5} + \frac{- 2}{5} \cdot (5 \cdot - 32)$

Step 5.2.1.1.3.4

Rewrite the expression.

$p = - \frac{q \cdot 2}{5} - 2 \cdot - 32$

Step 5.2.1.1.4

Multiply $- 2$ by $- 32$ .

$p = - \frac{q \cdot 2}{5} + 64$

Step 5.2.1.2

Move $2$ to the left of $q$ .

$p = - \frac{2 q}{5} + 64$