Solve for n 1/4(2n-28)=10

$\frac{1}{4} (2 n - 28) = 10$

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (2 n - 28)) = 4 \cdot 10$

Simplify both sides of the equation.

Simplify the left side.

Simplify $4 (\frac{1}{4} \cdot (2 n - 28))$ .

Apply the distributive property.

$4 (\frac{1}{4} (2 n) + \frac{1}{4} \cdot - 28) = 4 \cdot 10$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$4 (\frac{1}{2 (2)} (2 n) + \frac{1}{4} \cdot - 28) = 4 \cdot 10$

Factor $2$ out of $2 n$ .

$4 (\frac{1}{2 (2)} (2 (n)) + \frac{1}{4} \cdot - 28) = 4 \cdot 10$

Cancel the common factor.

$4 (\frac{1}{2 \cdot 2} (2 n) + \frac{1}{4} \cdot - 28) = 4 \cdot 10$

Rewrite the expression.

$4 (\frac{1}{2} n + \frac{1}{4} \cdot - 28) = 4 \cdot 10$

Combine $\frac{1}{2}$ and $n$ .

$4 (\frac{n}{2} + \frac{1}{4} \cdot - 28) = 4 \cdot 10$

Cancel the common factor of $4$ .

Factor $4$ out of $- 28$ .

$4 (\frac{n}{2} + \frac{1}{4} \cdot (4 (- 7))) = 4 \cdot 10$

Cancel the common factor.

$4 (\frac{n}{2} + \frac{1}{4} \cdot (4 \cdot - 7)) = 4 \cdot 10$

Rewrite the expression.

$4 (\frac{n}{2} - 7) = 4 \cdot 10$

Apply the distributive property.

$4 \frac{n}{2} + 4 \cdot - 7 = 4 \cdot 10$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) \frac{n}{2} + 4 \cdot - 7 = 4 \cdot 10$

Cancel the common factor.

$2 \cdot 2 \frac{n}{2} + 4 \cdot - 7 = 4 \cdot 10$

Rewrite the expression.

$2 n + 4 \cdot - 7 = 4 \cdot 10$

Multiply $4$ by $- 7$ .

$2 n - 28 = 4 \cdot 10$

Simplify the right side.

Multiply $4$ by $10$ .

$2 n - 28 = 40$

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

Add $28$ to both sides of the equation.

$2 n = 40 + 28$

Add $40$ and $28$ .

$2 n = 68$

Divide each term in $2 n = 68$ by $2$ and simplify.

Divide each term in $2 n = 68$ by $2$ .

$\frac{2 n}{2} = \frac{68}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{68}{2}$

Divide $n$ by $1$ .

$n = \frac{68}{2}$

Simplify the right side.

Divide $68$ by $2$ .

$n = 34$

Solve for n 1/4(2n-28)=10

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