Probably a stupid question

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In summary, the conversation discusses solving for a given inequality using interval notation. The speaker mentions making four cases and obtaining the final answer of [-7,-2),(3,8]. However, upon checking, it is found that none of the numbers between -7 and -2 work. The speaker then realizes a simpler method of solving for x and obtains the answer of 3 < x ≤ 8. The conversation ends with the speaker reflecting on their previous method and realizing the easier way of solving the problem.
  • #1
In interval notation, I was asked to solve for 5 < 2x - 1 ≤ 15

I did this by making the 4 cases...

2x-1>5 or 2x-1<-5 AND 2x-1≤ 15 and 2x-1≥-15
x > 3 or x < -2 AND x ≤ 8 and x ≥ -7

So for my final answer...i got [-7,-2),(3,8]

But when i check it, none of the numbers between -7 and -2 check...what'd I do wrong?

Lastly, is the answer actually just (3,8]?
 
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  • #2
What's the use in checking if 2x-1<-5 and 2x-1>= -15?
 
  • #3
honestly...I have no idea, but we were taught to make four cases for those...so that's how I've been doing it ever since.
 
  • #4
Actually, I just realized that I could've solved for x by adding 1 to the left and right, and dividing by 2 to the left and right...which gives me an answer of 3 < x ≤ 8...i'm pretty sure that's right...guess i went about it the wrong way
 
  • #5
Actually, I just realized that I could've solved for x by adding 1 to the left and right, and dividing by 2 to the left and right...which gives me an answer of 3 < x ≤ 8

Yup, that's probably the easiest way.
 
  • #6
I have no idea, but we were taught to make four cases for those...so that's how I've been doing it ever since.

You're probably confusing it with a problem like:

[tex]2 < |2x - 1| \le 15[/tex]

where the absolute value sign creates a problem.
 

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