MHB Can You Solve x|x+2|<5 by Subtracting 4?

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The discussion centers on solving the inequality |x + 2| < 5 and whether subtracting 4 is a valid step in the process. The correct approach involves rewriting the inequality as -5 < x + 2 < 5, then simplifying to -9 < x - 2 < 1. The confusion arises from the transition from x + 2 to x - 2, which necessitates subtracting 4. The final conclusion confirms that the steps taken are correct and necessary for solving the inequality.
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See picture for question.

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RTCNTC said:
See picture for question.

You recently posted a question quite similar to this one and received a thorough answer. Could you highlight what you are having trouble with here?
 
Joppy said:
You recently posted a question quite similar to this one and received a thorough answer. Could you highlight what you are having trouble with here?

I was not able to read Country Boy's reply because his words blocked most of the LaTex.
 
Joppy said:
You recently posted a question quite similar to this one and received a thorough answer. Could you highlight what you are having trouble with here?

I made a typo. There should be no x in front of the absolute value bar.

Solution:

|x + 2| < 5

-5 < x + 2 < 5

-5 - 4 < x + 2 - 4 < 5 - 4

-9 < x - 2 < 1

a = -9, b = 1

Is this correct?
 
Joppy said:
You recently posted a question quite similar to this one and received a thorough answer. Could you highlight what you are having trouble with here?

A friend responded to my question this way:

|x + 2| < 5

-5 < x + 2 < 5

-5 - 4 < x + 2 - 4 < 5 - 4

-9 < x - 2 < 1

a = -9, b = 1

Is this correct?

Where did 4 come from in his reply?
 
Yes, that is correct. In the original problem, you were given information about x+ 2. The problem asked for information about x- 2. To go from x+ 2 to x- 2, you need to subtract 4: (x+ 2)- 4= x+ (2- 4)= x- 2.
 
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