Solve for p 1/6(p+24)=10

$\frac{1}{6} (p + 24) = 10$

Step 1

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} \cdot (p + 24)) = 6 \cdot 10$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $6 (\frac{1}{6} \cdot (p + 24))$ .

Apply the distributive property.

$6 (\frac{1}{6} p + \frac{1}{6} \cdot 24) = 6 \cdot 10$

Combine $\frac{1}{6}$ and $p$ .

$6 (\frac{p}{6} + \frac{1}{6} \cdot 24) = 6 \cdot 10$

Cancel the common factor of $6$ .

Factor $6$ out of $24$ .

$6 (\frac{p}{6} + \frac{1}{6} \cdot (6 (4))) = 6 \cdot 10$

Cancel the common factor.

$6 (\frac{p}{6} + \frac{1}{6} \cdot (6 \cdot 4)) = 6 \cdot 10$

Rewrite the expression.

$6 (\frac{p}{6} + 4) = 6 \cdot 10$

Apply the distributive property.

$6 \frac{p}{6} + 6 \cdot 4 = 6 \cdot 10$

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{p}{6} + 6 \cdot 4 = 6 \cdot 10$

Rewrite the expression.

$p + 6 \cdot 4 = 6 \cdot 10$

Multiply $6$ by $4$ .

$p + 24 = 6 \cdot 10$

Simplify the right side.

Multiply $6$ by $10$ .

$p + 24 = 60$

Step 3

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

Subtract $24$ from both sides of the equation.

$p = 60 - 24$

Subtract $24$ from $60$ .

$p = 36$