Precalculus Examples

$\frac{3 x - 1}{x - 2} = 4$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$x - 2, 1$

Step 1.2

Remove parentheses.

$x - 2, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x - 2$

Step 2

Multiply each term in $\frac{3 x - 1}{x - 2} = 4$ by $x - 2$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{3 x - 1}{x - 2} = 4$ by $x - 2$ .

$\frac{3 x - 1}{x - 2} (x - 2) = 4 (x - 2)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x - 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x - 1}{x - 2} (x - 2) = 4 (x - 2)$

Step 2.2.1.2

Rewrite the expression.

$3 x - 1 = 4 (x - 2)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$3 x - 1 = 4 x + 4 \cdot - 2$

Step 2.3.2

Multiply $4$ by $- 2$ .

$3 x - 1 = 4 x - 8$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

Subtract $4 x$ from both sides of the equation.

$3 x - 1 - 4 x = - 8$

Step 3.1.2

Subtract $4 x$ from $3 x$ .

$- x - 1 = - 8$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$- x = - 8 + 1$

Step 3.2.2

Add $- 8$ and $1$ .

$- x = - 7$

Step 3.3

Divide each term in $- x = - 7$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = - 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 7}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 7}{- 1}$

Step 3.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 7}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 7$ by $- 1$ .

$x = 7$