Algebra Examples

$- \frac{1}{4} (p + 16) = 2$

Step 1

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{1}{4} \cdot (p + 16)) = - 4 \cdot 2$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- 4 (- \frac{1}{4} \cdot (p + 16))$ .

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Step 2.1.1.1

Apply the distributive property.

$- 4 (- \frac{1}{4} p - \frac{1}{4} \cdot 16) = - 4 \cdot 2$

Step 2.1.1.2

Combine $p$ and $\frac{1}{4}$ .

$- 4 (- \frac{p}{4} - \frac{1}{4} \cdot 16) = - 4 \cdot 2$

Step 2.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$- 4 (- \frac{p}{4} + \frac{- 1}{4} \cdot 16) = - 4 \cdot 2$

Step 2.1.1.3.2

Factor $4$ out of $16$ .

$- 4 (- \frac{p}{4} + \frac{- 1}{4} \cdot (4 (4))) = - 4 \cdot 2$

Step 2.1.1.3.3

Cancel the common factor.

$- 4 (- \frac{p}{4} + \frac{- 1}{4} \cdot (4 \cdot 4)) = - 4 \cdot 2$

Step 2.1.1.3.4

Rewrite the expression.

$- 4 (- \frac{p}{4} - 1 \cdot 4) = - 4 \cdot 2$

Step 2.1.1.4

Multiply $- 1$ by $4$ .

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $4$ .

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Step 2.1.1.6.1

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

$- 4 \frac{- p}{4} - 4 \cdot - 4 = - 4 \cdot 2$

Step 2.1.1.6.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- p}{4} - 4 \cdot - 4 = - 4 \cdot 2$

Step 2.1.1.6.3

Cancel the common factor.

$4 \cdot - 1 \frac{- p}{4} - 4 \cdot - 4 = - 4 \cdot 2$

Step 2.1.1.6.4

Rewrite the expression.

$- - p - 4 \cdot - 4 = - 4 \cdot 2$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 1$ by $- 1$ .

$1 p - 4 \cdot - 4 = - 4 \cdot 2$

Step 2.1.1.7.2

Multiply $p$ by $1$ .

$p - 4 \cdot - 4 = - 4 \cdot 2$

Step 2.1.1.7.3

Multiply $- 4$ by $- 4$ .

$p + 16 = - 4 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 4$ by $2$ .

$p + 16 = - 8$

Step 3

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

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Step 3.1

Subtract $16$ from both sides of the equation.

$p = - 8 - 16$

Step 3.2

Subtract $16$ from $- 8$ .

$p = - 24$