Question about this linear equation with fractions

In summary, the conversation involves using 2x - 4 as the LCD and simplifying an equation to solve for x. The mistake was found and corrected, resulting in x = 3. The mistake was made due to a careless error in writing down the equation.
  • #1
hackedagainanda
52
11
Homework Statement
8/(x - 2) - (13/2) = 3/(2x - 4)
Relevant Equations
None.
I use 2x -4 as the LCD and turn 8/(x - 2) - (13/2) = 3 into 16 - 13x - 4 = 3, I then get 12 - 13x = 3 which leads me to 13x = -9 so x = -9/13 which is the wrong answer.

Where did I make a mistake?
 
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  • #2
I found my mistake, (-13/2) * 2x -4 is - 13(x - 2) = 13x + 26 so then its 16 + 26 = 42 + 13x = 3 and then 42 - 3 = 39 then 13x = 39 so x is 3.
 
  • #3
hackedagainanda said:
I found my mistake, (-13/2) * 2x -4 is - 13(x - 2) = 13x + 26 so then its 16 + 26 = 42 + 13x = 3 and then 42 - 3 = 39 then 13x = 39 so x is 3.
The solution may be x = 3, but you have several errors.

−13(x − 2) = −13x +26 .

That gives the Left Hand Side as being:
(2x − 4)(8/(x − 2) − (13/2)) which is 16 + 26 − 13x and finally 42 − 13x

The Right Hand Side becomes 3.
 
  • #4
Thanks for the tip, I was sloppy when writing down the equation. I need to slow down and make sure all the signs are correct.
 
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Related to Question about this linear equation with fractions

1. What is a linear equation with fractions?

A linear equation with fractions is an algebraic equation that contains at least one fraction and has a degree of one. It can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

2. How do you solve a linear equation with fractions?

To solve a linear equation with fractions, you can use the following steps:

  • Clear the fractions by multiplying both sides of the equation by the common denominator.
  • Combine like terms on both sides of the equation.
  • Isolate the variable on one side of the equation by using inverse operations.
  • Simplify the equation to find the value of the variable.

3. Can a linear equation with fractions have more than one solution?

Yes, a linear equation with fractions can have more than one solution. This is because the slope of the equation can be the same for multiple values of the variable, resulting in different solutions.

4. What is the importance of linear equations with fractions in real life?

Linear equations with fractions are important in real life because they can be used to model and solve various real-world problems. For example, they can be used to calculate the cost of a product with a given discount, or to determine the amount of ingredients needed for a recipe.

5. How can I check if my solution to a linear equation with fractions is correct?

You can check if your solution to a linear equation with fractions is correct by substituting the value of the variable into the original equation and simplifying both sides. If the resulting values are equal, then your solution is correct.

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