Solve for n (4n-2)/(2n)=7

$\frac{4 n - 2}{2 n} = 7$

Step 1

Factor each term.

Factor $2$ out of $4 n - 2$ .

Factor $2$ out of $4 n$ .

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

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (2 n) + 2 (- 1)$ .

$\frac{2 (2 n - 1)}{2 n} = 7$

Reduce the expression $\frac{2 (2 n - 1)}{2 n}$ by cancelling the common factors.

Cancel the common factor.

$\frac{2 (2 n - 1)}{2 n} = 7$

Rewrite the expression.

$\frac{2 n - 1}{n} = 7$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$n, 1$

The LCM of one and any expression is the expression.

$n$

Step 3

Multiply each term in $\frac{2 n - 1}{n} = 7$ by $n$ to eliminate the fractions.

Multiply each term in $\frac{2 n - 1}{n} = 7$ by $n$ .

$\frac{2 n - 1}{n} n = 7 n$

Simplify the left side.

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{2 n - 1}{n} n = 7 n$

Rewrite the expression.

$2 n - 1 = 7 n$

Step 4

Solve the equation.

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

Subtract $7 n$ from both sides of the equation.

$2 n - 1 - 7 n = 0$

Subtract $7 n$ from $2 n$ .

$- 5 n - 1 = 0$

Add $1$ to both sides of the equation.

$- 5 n = 1$

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

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

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$n = - 0.2$

Solve for n (4n-2)/(2n)=7

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