Pre-Algebra Examples

$Q = \frac{8}{7} p + 30$

Step 1

Rewrite the equation as $\frac{8}{7} p + 30 = Q$ .

$\frac{8}{7} p + 30 = Q$

Step 2

Combine $\frac{8}{7}$ and $p$ .

$\frac{8 p}{7} + 30 = Q$

Step 3

Subtract $30$ from both sides of the equation.

$\frac{8 p}{7} = Q - 30$

Step 4

Multiply both sides of the equation by $\frac{7}{8}$ .

$\frac{7}{8} \cdot \frac{8 p}{7} = \frac{7}{8} (Q - 30)$

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 $\frac{7}{8} \cdot \frac{8 p}{7}$ .

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Step 5.1.1.1

Cancel the common factor of $7$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{7}{8} \cdot \frac{8 p}{7} = \frac{7}{8} (Q - 30)$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 p) = \frac{7}{8} (Q - 30)$

Step 5.1.1.2

Cancel the common factor of $8$ .

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Step 5.1.1.2.1

Factor $8$ out of $8 p$ .

$\frac{1}{8} (8 (p)) = \frac{7}{8} (Q - 30)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 p) = \frac{7}{8} (Q - 30)$

Step 5.1.1.2.3

Rewrite the expression.

$p = \frac{7}{8} (Q - 30)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{7}{8} (Q - 30)$ .

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Step 5.2.1.1

Apply the distributive property.

$p = \frac{7}{8} Q + \frac{7}{8} \cdot - 30$

Step 5.2.1.2

Combine $\frac{7}{8}$ and $Q$ .

$p = \frac{7 Q}{8} + \frac{7}{8} \cdot - 30$

Step 5.2.1.3

Cancel the common factor of $2$ .

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Step 5.2.1.3.1

Factor $2$ out of $8$ .

$p = \frac{7 Q}{8} + \frac{7}{2 (4)} \cdot - 30$

Step 5.2.1.3.2

Factor $2$ out of $- 30$ .

$p = \frac{7 Q}{8} + \frac{7}{2 \cdot 4} \cdot (2 \cdot - 15)$

Step 5.2.1.3.3

Cancel the common factor.

$p = \frac{7 Q}{8} + \frac{7}{2 \cdot 4} \cdot (2 \cdot - 15)$

Step 5.2.1.3.4

Rewrite the expression.

$p = \frac{7 Q}{8} + \frac{7}{4} \cdot - 15$

Step 5.2.1.4

Combine $\frac{7}{4}$ and $- 15$ .

$p = \frac{7 Q}{8} + \frac{7 \cdot - 15}{4}$

Step 5.2.1.5

Simplify the expression.

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Step 5.2.1.5.1

Multiply $7$ by $- 15$ .

$p = \frac{7 Q}{8} + \frac{- 105}{4}$

Step 5.2.1.5.2

Move the negative in front of the fraction.

$p = \frac{7 Q}{8} - \frac{105}{4}$