Solve for n 3/4n-18=1/4n-4

$\frac{3}{4} n - 18 = \frac{1}{4} n - 4$

Step 1

Combine $\frac{3}{4}$ and $n$ .

$\frac{3 n}{4} - 18 = \frac{1}{4} n - 4$

Step 2

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

$\frac{3 n}{4} - 18 = \frac{n}{4} - 4$

Step 3

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

Subtract $\frac{n}{4}$ from both sides of the equation.

$\frac{3 n}{4} - 18 - \frac{n}{4} = - 4$

Combine the numerators over the common denominator.

$- 18 + \frac{3 n - n}{4} = - 4$

Subtract $n$ from $3 n$ .

$- 18 + \frac{2 n}{4} = - 4$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 n$ .

$- 18 + \frac{2 (n)}{4} = - 4$

Cancel the common factors.

Factor $2$ out of $4$ .

$- 18 + \frac{2 n}{2 \cdot 2} = - 4$

Cancel the common factor.

$- 18 + \frac{2 n}{2 \cdot 2} = - 4$

Rewrite the expression.

$- 18 + \frac{n}{2} = - 4$

Step 4

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

Add $18$ to both sides of the equation.

$\frac{n}{2} = - 4 + 18$

Add $- 4$ and $18$ .

$\frac{n}{2} = 14$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{n}{2} = 2 \cdot 14$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{n}{2} = 2 \cdot 14$

Rewrite the expression.

$n = 2 \cdot 14$

Simplify the right side.

Multiply $2$ by $14$ .

$n = 28$