anonymous
  • anonymous
Someone help me out here? What is the solution set of the absolute value sentence |x - 6| = -10? A. {4/3, -4} B. {x|x > 4 or x < -4/5} C. No Solution D. {x|-11 < x < -7} E. All Real Numbers
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Mertsj
  • Mertsj
What do you know about absolute values?
anonymous
  • anonymous
Not very much.
Mertsj
  • Mertsj
Try to think of one thing. What is the absolute value of 3?

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anonymous
  • anonymous
That's not true.
Mertsj
  • Mertsj
Then tell me what the absolute value of 3 is.
anonymous
  • anonymous
You tell me
Mertsj
  • Mertsj
So there is your problem. The absolute value of a number is either the number or its opposite, whichever is positive.
Mertsj
  • Mertsj
So the absolute value of 3 is either 3 or the opposite of 3, whichever one is positive. So what is the absolute value of 3?
anonymous
  • anonymous
either 3 or negative 3 lol that's what you just told me rite?
Mertsj
  • Mertsj
So your job is to pick which one is the positive one. Remember...I said either 3 or negative three, whichever one is positive.
Mertsj
  • Mertsj
So what is the absolute value of 3?
anonymous
  • anonymous
3
Mertsj
  • Mertsj
Yes. The absolute value of 3 is 3. What is the absolute value of -3? Remember it is either 3 or -3. Whichever one is positive.
anonymous
  • anonymous
3 but how is this helping me get my answer?
Mertsj
  • Mertsj
I am the teacher and you are the student. So just answer my questions.
Mertsj
  • Mertsj
What is the absolute value of 15?
anonymous
  • anonymous
15
Mertsj
  • Mertsj
What is the absolute value of -15?
anonymous
  • anonymous
15
Mertsj
  • Mertsj
So what can you tell me about all absolute values?
anonymous
  • anonymous
the number will always be positive
Mertsj
  • Mertsj
very good. So if I said to you, "Think of a number whose absolute value is -8" What would you say to me?
anonymous
  • anonymous
The number would be 8.
Mertsj
  • Mertsj
Read my question again: Think of a number whose absolute value is NEGATIVE 8
Mertsj
  • Mertsj
did you not just tell me that an absolute value will always be positive?
anonymous
  • anonymous
Ohhhh, i guess it's not alway's going to be :/ Either that question is wrong or i am wrong.
Mertsj
  • Mertsj
The absolute value IS always POSITIVE. Repeat that statement to yourself 50 times.
anonymous
  • anonymous
So than what you asked me is impossible?
anonymous
  • anonymous
the negative 8 thing
Mertsj
  • Mertsj
YEAH!!!!! You got it!!!!!
Mertsj
  • Mertsj
So If I say to you, "think of a number whose absolute value is -8", you should say, "There is no such number."
anonymous
  • anonymous
Yes :)
Mertsj
  • Mertsj
\[|x-6|=-10\]
Mertsj
  • Mertsj
Now look at your problem. See what it say? It says the absolute value is equal to -10
Mertsj
  • Mertsj
So what do you say back to your problem?
anonymous
  • anonymous
So theres no solution?
Mertsj
  • Mertsj
Way to go!!! And thanks for sticking with me. Isn't learning fun?????
anonymous
  • anonymous
Lol i guess so.
anonymous
  • anonymous
So what about this one?
anonymous
  • anonymous
What is the solution set of the absolute value sentence |x + 9| < 2? A. {4/3, -4} B. {x|x > 4 or x < -4/5} C. No Solution D. {x|-11 < x < -7} E. All Real Numbers
Mertsj
  • Mertsj
Ok. Now think of a number line. Where are the numbers that have absolute value that is less than 2?
anonymous
  • anonymous
To the left
Mertsj
  • Mertsj
|dw:1333506174089:dw|
Mertsj
  • Mertsj
Put you pencil on one of those numbers and ask yourself "What is the absolute value of this number?" And keep doing that until you find some that the answer is less that 2.
Mertsj
  • Mertsj
How about 3? Does that work?
Mertsj
  • Mertsj
Is the absolute value of 3 less than 2?
anonymous
  • anonymous
When i look at the answers none of them make sense to me at all. And no it's 3
Mertsj
  • Mertsj
You're getting ahead of me here. All we are trying to do is think of the numbers whose absolute value is less than two.
anonymous
  • anonymous
The only number that is less than too but is still absolute is 1.
Mertsj
  • Mertsj
|dw:1333506448047:dw|
Mertsj
  • Mertsj
See those numbers I have marked on that graph? All of those numbers have absolute value that is less than 2.
anonymous
  • anonymous
I dont get how, 5 is more than 2
Mertsj
  • Mertsj
So some of them are -1, -1.5, 0, 1, 1,3, 1.99 and so on.
Mertsj
  • Mertsj
Would you rather have 5 dollars or 2 dollars?
anonymous
  • anonymous
5 but you said numbers less than 2......
Mertsj
  • Mertsj
Yes. The numbers between -2 and 2 have absolute values that are less than 2. That's all I'm saying.
Mertsj
  • Mertsj
|dw:1333506692449:dw|
anonymous
  • anonymous
But negatives aren't Absolute, that's what you taught me
Mertsj
  • Mertsj
But negative numbers have absolute values. If you look back you will see that you correctly told me that the absolute value of -3 is 3. And that is correct.
Mertsj
  • Mertsj
So all of the numbers between -2 and 2 have absolute values that are less than 2
Mertsj
  • Mertsj
Are you with me?
anonymous
  • anonymous
Yea sorry
Mertsj
  • Mertsj
So your problem says that the absolute value of x+9 is less than 2. That means that x+9 has to be between -2 and 2
Mertsj
  • Mertsj
|dw:1333507179451:dw|
Mertsj
  • Mertsj
So we can write: |dw:1333507250555:dw|
Mertsj
  • Mertsj
|dw:1333507286385:dw|
anonymous
  • anonymous
ok soooooo?
Mertsj
  • Mertsj
So choose option D
anonymous
  • anonymous
How did you get 2 out of that whole thing though? In the beginning
Mertsj
  • Mertsj
Because the problem says that the absolute value is less than 2.
anonymous
  • anonymous
oh... sorry.
Mertsj
  • Mertsj
If x+9 is 3 that won't work because the absolute value of 3 is NOT less than 2.
Mertsj
  • Mertsj
If x+9 is -2.1, that won't work because the absolute value of -2.1 is NOT less than 2
Mertsj
  • Mertsj
So x+9 has to be between 2 and -2
anonymous
  • anonymous
ok

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