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

  • MHB
  • Thread starter mathdad
  • Start date
In summary, the friend's response correctly solved the problem by using basic algebraic principles, including subtracting 4 from both sides to isolate x- 2 and finding the values of a and b.
  • #1
mathdad
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See picture for question.

View attachment 8538
 

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  • #2
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?
 
  • #3
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.
 
  • #4
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?
 
  • #5
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?
 
  • #6
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.
 

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

What does the equation "solve x|x+2|<5 for x-2" mean?

The equation is asking for the values of x that make the inequality x|x+2|<5 true when x is subtracted by 2.

How do I solve this equation?

To solve this equation, you can follow these steps:1. Simplify the absolute value expression by considering both positive and negative cases.2. Solve for x in the resulting inequality.3. Add 2 to the solutions to get the final values for x.

Can I use any value for x?

No, you cannot use any value for x. The values of x must make the inequality x|x+2|<5 true, otherwise they will not be considered as solutions.

Is there more than one solution for this equation?

Yes, there can be more than one solution for this equation since it is an inequality. The number of solutions will depend on the value of x and the inequality.

How can I check if my solution is correct?

You can check your solution by substituting it back into the original inequality. If it satisfies the inequality, then it is a valid solution. You can also graph the equation and see if the solution falls within the shaded region.

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