One inequality sign to two inequality signs

[Hancko]

Hello Tutors, I please request assistance with the following question:

I came up with the solution: x<7/4, but apparently this is incorrect. They gave me solutions in the format of a>x>b. I am confused as to how to get this format.

 

[lev888]

Hello Tutors, I please request assistance with the following question:
View attachment 25312
I came up with the solution: x<7/4, but apparently this is incorrect. They gave me solutions in the format of a>x>b. I am confused as to how to get this format.

Please post your solution.

 

[Dr.Peterson]

Hello Tutors, I please request assistance with the following question:
View attachment 25312
I came up with the solution: x<7/4, but apparently this is incorrect. They gave me solutions in the format of a>x>b. I am confused as to how to get this format.

It looks like you probably multiplied both sides by x-2. You can't do that without taking into account whether x-2 is positive or negative. You can either use two cases in your work, or use a different traditional method for rational inequalities that starts with subtracting 5 from both sides, simplifies, and then considers the sign of the numerator and denominator.

 

[Hancko]

Please post your solution.

My solution is: x<7/4, but this is incorrect.

 

[Hancko]

It looks like you probably multiplied both sides by x-2. You can't do that without taking into account whether x-2 is positive or negative. You can either use two cases in your work, or use a different traditional method for rational inequalities that starts with subtracting 5 from both sides, simplifies, and then considers the sign of the numerator and denominator.

I am afraid I do not understand. Why do I subtract 5 from both sides?

 

[lev888]

My solution is: x<7/4, but this is incorrect.

x<7/4 is your answer, not solution. Please post your _work_.

 

[Dr.Peterson]

I am afraid I do not understand. Why do I subtract 5 from both sides?

What have you been taught about solving rational inequalities? As I said, there are a couple ways to do it.

Here is what I am referring to:

Algebra - Rational Inequalities

We continue solving inequalities in this section. We now will solve inequalities that involve rational expressions, although as we’ll see the process here is pretty much identical to the process used when solving inequalities with polynomials.

tutorial.math.lamar.edu

Your problem is like example 4; if you haven't been taught this method, you'll want to work through the whole page, and possibly the preceeding section.​

Solving Rational Inequalities - MathBitsNotebook(A2)

mathbitsnotebook.com

That shows two methods, with the same example; the second is similar to the case method I mentioned, but more like the other.​

http://jongarvin.com/up/MHF4U/slides/rational_inequalities_handout.pdf

That shows the case method fully, followed by a short example of the interval method. If you carried out what I assume you did, correctly, you would need to use cases.​

 

[Hancko]

Please post your solution.

I have completed the question with Peterson's reference to the other website. Is this correct?

What have you been taught about solving rational inequalities? As I said, there are a couple ways to do it.

Here is what I am referring to:

Algebra - Rational Inequalities

We continue solving inequalities in this section. We now will solve inequalities that involve rational expressions, although as we’ll see the process here is pretty much identical to the process used when solving inequalities with polynomials.

tutorial.math.lamar.edu

Your problem is like example 4; if you haven't been taught this method, you'll want to work through the whole page, and possibly the preceding section.​

Solving Rational Inequalities - MathBitsNotebook(A2)

mathbitsnotebook.com

That shows two methods, with the same example; the second is similar to the case method I mentioned, but more like the other.​

http://jongarvin.com/up/MHF4U/slides/rational_inequalities_handout.pdf

That shows the case method fully, followed by a short example of the interval method. If you carried out what I assume you did, correctly, you would need to use cases.​

I have completed the question with your reference to the other website. Is this correct?

Thank you for all of your support.

 

[Dr.Peterson]

Looks good.

 

[HallsofIvy]

Your real problem is a simple arithmetic error! x- 5x is -4x, not -6x.

 

[Dr.Peterson]

Your real problem is a simple arithmetic error! x- 5x is -4x, not -6x.

Hancko did write -4x, as you can see later. You're just misreading it.