Solve for n 3/4-1/2n=5/8

$\frac{3}{4} - \frac{1}{2} n = \frac{5}{8}$

Step 1

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

$\frac{3}{4} - \frac{n}{2} = \frac{5}{8}$

Step 2

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

Subtract $\frac{3}{4}$ from both sides of the equation.

$- \frac{n}{2} = \frac{5}{8} - \frac{3}{4}$

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{n}{2} = \frac{5}{8} - \frac{3}{4} \cdot \frac{2}{2}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$- \frac{n}{2} = \frac{5}{8} - \frac{3 \cdot 2}{4 \cdot 2}$

Multiply $4$ by $2$ .

$- \frac{n}{2} = \frac{5}{8} - \frac{3 \cdot 2}{8}$

Combine the numerators over the common denominator.

$- \frac{n}{2} = \frac{5 - 3 \cdot 2}{8}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$- \frac{n}{2} = \frac{5 - 6}{8}$

Subtract $6$ from $5$ .

$- \frac{n}{2} = \frac{- 1}{8}$

Move the negative in front of the fraction.

$- \frac{n}{2} = - \frac{1}{8}$

Step 3

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{n}{2}) = - 2 (- \frac{1}{8})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{n}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{n}{2}$ into the numerator.

$- 2 \frac{- n}{2} = - 2 (- \frac{1}{8})$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- n}{2} = - 2 (- \frac{1}{8})$

Cancel the common factor.

$2 \cdot - 1 \frac{- n}{2} = - 2 (- \frac{1}{8})$

Rewrite the expression.

$- - n = - 2 (- \frac{1}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - 2 (- \frac{1}{8})$

Multiply $n$ by $1$ .

$n = - 2 (- \frac{1}{8})$

Simplify the right side.

Simplify $- 2 (- \frac{1}{8})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$n = - 2 (\frac{- 1}{8})$

Factor $2$ out of $- 2$ .

$n = 2 (- 1) \frac{- 1}{8}$

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Multiply $- - \frac{1}{4}$ .

Multiply $- 1$ by $- 1$ .

$n = 1 (\frac{1}{4})$

Multiply $\frac{1}{4}$ by $1$ .

$n = \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{4}$

Decimal Form:

$n = 0.25$

Solve for n 3/4-1/2n=5/8

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