Algebra Examples

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

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

Step 1

Factor each term.

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Step 1.1

Factor

2

$2$ out of

4 n - 2

$4 n - 2$ .

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Step 1.1.1

Factor

2

$2$ out of

4 n

$4 n$ .

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

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

Step 1.1.2

Factor

2

$2$ out of

- 2

$- 2$ .

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

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

Step 1.1.3

Factor

$2$ out of

$2 (2 n) + 2 (- 1)$ .

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

Step 1.2

Reduce the expression

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

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$n, 1$

Step 2.2

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.

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Step 3.1

Multiply each term in

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

$n$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

$n$ .

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Step 3.2.1.1

Move the leading negative in

$- \frac{2 n - 1}{n}$ into the numerator.

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

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

$- (2 n - 1) = 7 n$

Step 3.2.2

Apply the distributive property.

$- (2 n) - - 1 = 7 n$

Step 3.2.3

Multiply.

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Step 3.2.3.1

Multiply

$2$ by

$- 1$ .

$- 2 n - - 1 = 7 n$

Step 3.2.3.2

Multiply

$- 1$ by

$- 1$ .

$- 2 n + 1 = 7 n$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing

$n$ to the left side of the equation.

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Step 4.1.1

Subtract

$7 n$ from both sides of the equation.

$- 2 n + 1 - 7 n = 0$

Step 4.1.2

Subtract

$7 n$ from

$- 2 n$ .

$- 9 n + 1 = 0$

Step 4.2

Subtract

$1$ from both sides of the equation.

$- 9 n = - 1$

Step 4.3

Divide each term in

$- 9 n = - 1$ by

$- 9$ and simplify.

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Step 4.3.1

Divide each term in

$- 9 n = - 1$ by

$- 9$ .

$\frac{- 9 n}{- 9} = \frac{- 1}{- 9}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of

$- 9$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 9 n}{- 9} = \frac{- 1}{- 9}$

Step 4.3.2.1.2

Divide

$n$ by

$1$ .

$n = \frac{- 1}{- 9}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Dividing two negative values results in a positive value.

$n = \frac{1}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{9}$

Decimal Form:

$n = 0.\overline{1}$