Pre-Algebra Examples

$- 24 - \frac{1}{8} p = \frac{3}{8} p$

Step 1

Combine $p$ and $\frac{1}{8}$ .

$- 24 - \frac{p}{8} = \frac{3}{8} p$

Step 2

Combine $\frac{3}{8}$ and $p$ .

$- 24 - \frac{p}{8} = \frac{3 p}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{3 p}{8}$ from both sides of the equation.

$- 24 - \frac{p}{8} - \frac{3 p}{8} = 0$

Step 3.2

Combine the numerators over the common denominator.

$- 24 + \frac{- p - 3 p}{8} = 0$

Step 3.3

Subtract $3 p$ from $- p$ .

$- 24 + \frac{- 4 p}{8} = 0$

Step 3.4

Simplify each term.

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Step 3.4.1

Cancel the common factor of $- 4$ and $8$ .

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Step 3.4.1.1

Factor $4$ out of $- 4 p$ .

$- 24 + \frac{4 (- p)}{8} = 0$

Step 3.4.1.2

Cancel the common factors.

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Step 3.4.1.2.1

Factor $4$ out of $8$ .

$- 24 + \frac{4 (- p)}{4 (2)} = 0$

Step 3.4.1.2.2

Cancel the common factor.

$- 24 + \frac{4 (- p)}{4 \cdot 2} = 0$

Step 3.4.1.2.3

Rewrite the expression.

$- 24 + \frac{- p}{2} = 0$

Step 3.4.2

Move the negative in front of the fraction.

$- 24 - \frac{p}{2} = 0$

Step 4

Add $24$ to both sides of the equation.

$- \frac{p}{2} = 24$

Step 5

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{p}{2}) = - 2 \cdot 24$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

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

$- 2 \frac{- p}{2} = - 2 \cdot 24$

Step 6.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- p}{2} = - 2 \cdot 24$

Step 6.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- p}{2} = - 2 \cdot 24$

Step 6.1.1.1.4

Rewrite the expression.

$- - p = - 2 \cdot 24$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 p = - 2 \cdot 24$

Step 6.1.1.2.2

Multiply $p$ by $1$ .

$p = - 2 \cdot 24$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 2$ by $24$ .

$p = - 48$