Solve for n 7/8-1/4n=-3/8

$\frac{7}{8} - \frac{1}{4} n = - \frac{3}{8}$

Step 1

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

$\frac{7}{8} - \frac{n}{4} = - \frac{3}{8}$

Step 2

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

Subtract $\frac{7}{8}$ from both sides of the equation.

$- \frac{n}{4} = - \frac{3}{8} - \frac{7}{8}$

Combine the numerators over the common denominator.

$- \frac{n}{4} = \frac{- 3 - 7}{8}$

Subtract $7$ from $- 3$ .

$- \frac{n}{4} = \frac{- 10}{8}$

Cancel the common factor of $- 10$ and $8$ .

Factor $2$ out of $- 10$ .

$- \frac{n}{4} = \frac{2 (- 5)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$- \frac{n}{4} = \frac{2 \cdot - 5}{2 \cdot 4}$

Cancel the common factor.

$- \frac{n}{4} = \frac{2 \cdot - 5}{2 \cdot 4}$

Rewrite the expression.

$- \frac{n}{4} = \frac{- 5}{4}$

Move the negative in front of the fraction.

$- \frac{n}{4} = - \frac{5}{4}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- n = - 5$

Step 4

Divide each term in $- n = - 5$ by $- 1$ and simplify.

Divide each term in $- n = - 5$ by $- 1$ .

$\frac{- n}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{- 5}{- 1}$

Divide $n$ by $1$ .

$n = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$n = 5$