trwatkins1
  • trwatkins1
Which values satisfy the inequality? |y| > 6 Choose all answers that are correct. A. y = –7 B. y = –1 C. y = 3 D. y = 9
Mathematics
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schrodinger
  • schrodinger
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trwatkins1
  • trwatkins1
@SolomonZelman
e.mccormick
  • e.mccormick
Well, yo can plug them in and try, but in general, whenever you see an absolute value inequality it means that the number will be constriend between two poiunts or NOT between those two points.
mathstudent55
  • mathstudent55
To solve an equation of the form \(|X| = k\) where X is an expression with a variable and k is a non-negative number, solve the compound equation X = k or X = -k

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e.mccormick
  • e.mccormick
|x| < k means x will be between k and -k. |x| > k means x will be outside k and -k.
mathstudent55
  • mathstudent55
Your expression with a variable is simply y. Set y equal to the number. Then set y equal to the negative of the number. Separate the equations with the word "or". That is the solution.
trwatkins1
  • trwatkins1
ok
e.mccormick
  • e.mccormick
So, based on all that, do you see the answer(s)?
trwatkins1
  • trwatkins1
???????????
mathstudent55
  • mathstudent55
Sorry. I misread the problem as as equation, y = |6|. Follow @e.mccormick as to how to find the answer the question.
trwatkins1
  • trwatkins1
what do you mean by |x| > k means x will be outside k and -k.
e.mccormick
  • e.mccormick
Because it is an inequality, y will be above or below some value. However, because y is in an absolute value, it means it is like being above or below two values: |x| > k means: x > k AND x > -k So if k is say 3, the line graph would be: |dw:1440444499449:dw| So it is OUTSIDE the -3 to 3 range.
Anas.P
  • Anas.P
|y|= y with a positive sign this means that |-7|=7 and |7|=7 get it? |-3|=3 and |3|=3. Now try.
e.mccormick
  • e.mccormick
If I did |x|<3, it would be: |dw:1440444653222:dw| That is inside...
e.mccormick
  • e.mccormick
Or between. That is what I meant by it is between the numbers or outside those numbers. The > or < tells you which.
trwatkins1
  • trwatkins1
>:( i still dont understand
e.mccormick
  • e.mccormick
OK. Well, lets do try and see. |y| > 6 y = –7 y = –1 y = 3 y = 9 If you put -7 in place of y, is that true? If yes, then that is a valid answer. If no, it is not. Then repeat with -1, 3, and 9.
trwatkins1
  • trwatkins1
@e.mccormick 9?
e.mccormick
  • e.mccormick
Yes, |9| > 6 is true. However, there is another.
trwatkins1
  • trwatkins1
3?
e.mccormick
  • e.mccormick
|3| > 6 3 > 6 Three is greater than six... no, that is false.
trwatkins1
  • trwatkins1
oh yea
e.mccormick
  • e.mccormick
Remember how the absolute value works.
trwatkins1
  • trwatkins1
so 7
e.mccormick
  • e.mccormick
Yes. |y| > 6 means values outside the range of -6 to 6 are true. So values more than 6 and les than -6 would satisfy that. -7 is less than -6, so it is true.
e.mccormick
  • e.mccormick
IF it had been |y| < 6, it would have been the other two. But for |y| > 6 it is A and D.
e.mccormick
  • e.mccormick
I hope that makes more sense now.
trwatkins1
  • trwatkins1
@e.mccormick 100%
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