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

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

Step 1

Simplify $- 3 + \frac{3}{2} n - \frac{1}{8} n + \frac{1}{2}$ .

Simplify each term.

Combine $\frac{3}{2}$ and $n$ .

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

Combine $n$ and $\frac{1}{8}$ .

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

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

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

Combine $- 3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $2$ .

$\frac{3 n}{2} - \frac{n}{8} + \frac{- 6 + 1}{2} = 2 n - \frac{5}{8}$

Add $- 6$ and $1$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

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

Multiply $2$ by $4$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $n$ out of $3 n \cdot 4 - n$ .

Factor $n$ out of $3 n \cdot 4$ .

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

Factor $n$ out of $- n$ .

$\frac{n (3 \cdot 4) + n \cdot - 1}{8} - \frac{5}{2} = 2 n - \frac{5}{8}$

Factor $n$ out of $n (3 \cdot 4) + n \cdot - 1$ .

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

Multiply $3$ by $4$ .

$\frac{n (12 - 1)}{8} - \frac{5}{2} = 2 n - \frac{5}{8}$

Subtract $1$ from $12$ .

$\frac{n \cdot 11}{8} - \frac{5}{2} = 2 n - \frac{5}{8}$

Move $11$ to the left of $n$ .

$\frac{11 n}{8} - \frac{5}{2} = 2 n - \frac{5}{8}$

Step 2

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

Subtract $2 n$ from both sides of the equation.

$\frac{11 n}{8} - \frac{5}{2} - 2 n = - \frac{5}{8}$

To write $- 2 n$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{11 n}{8} - 2 n \cdot \frac{8}{8} - \frac{5}{2} = - \frac{5}{8}$

Combine $- 2 n$ and $\frac{8}{8}$ .

$\frac{11 n}{8} + \frac{- 2 n \cdot 8}{8} - \frac{5}{2} = - \frac{5}{8}$

Combine the numerators over the common denominator.

$\frac{11 n - 2 n \cdot 8}{8} - \frac{5}{2} = - \frac{5}{8}$

Simplify each term.

Simplify the numerator.

Factor $n$ out of $11 n - 2 n \cdot 8$ .

Factor $n$ out of $11 n$ .

$\frac{n \cdot 11 - 2 n \cdot 8}{8} - \frac{5}{2} = - \frac{5}{8}$

Factor $n$ out of $- 2 n \cdot 8$ .

$\frac{n \cdot 11 + n (- 2 \cdot 8)}{8} - \frac{5}{2} = - \frac{5}{8}$

Factor $n$ out of $n \cdot 11 + n (- 2 \cdot 8)$ .

$\frac{n (11 - 2 \cdot 8)}{8} - \frac{5}{2} = - \frac{5}{8}$

Multiply $- 2$ by $8$ .

$\frac{n (11 - 16)}{8} - \frac{5}{2} = - \frac{5}{8}$

Subtract $16$ from $11$ .

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

Move $- 5$ to the left of $n$ .

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

Move the negative in front of the fraction.

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

Step 3

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

Add $\frac{5}{2}$ to both sides of the equation.

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

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

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

Multiply $\frac{5}{2}$ by $\frac{4}{4}$ .

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

Multiply $2$ by $4$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $4$ .

$- \frac{5 n}{8} = \frac{- 5 + 20}{8}$

Add $- 5$ and $20$ .

$- \frac{5 n}{8} = \frac{15}{8}$

Step 4

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

$- 5 n = 15$

Step 5

Divide each term in $- 5 n = 15$ by $- 5$ and simplify.

Divide each term in $- 5 n = 15$ by $- 5$ .

$\frac{- 5 n}{- 5} = \frac{15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 n}{- 5} = \frac{15}{- 5}$

Divide $n$ by $1$ .

$n = \frac{15}{- 5}$

Simplify the right side.

Divide $15$ by $- 5$ .

$n = - 3$

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

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