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

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- trwatkins1

- schrodinger

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- trwatkins1

- 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

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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## More answers

- e.mccormick

|x| < k means x will be between k and -k.
|x| > k means x will be outside k and -k.

- 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

ok

- e.mccormick

So, based on all that, do you see the answer(s)?

- trwatkins1

???????????

- mathstudent55

Sorry. I misread the problem as as equation, y = |6|.
Follow @e.mccormick as to how to find the answer the question.

- trwatkins1

what do you mean by |x| > k means x will be outside k and -k.

- 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

|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

If I did |x|<3, it would be:
|dw:1440444653222:dw|
That is inside...

- 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

>:( i still dont understand

- 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

@e.mccormick 9?

- e.mccormick

Yes, |9| > 6 is true. However, there is another.

- trwatkins1

3?

- e.mccormick

|3| > 6
3 > 6
Three is greater than six... no, that is false.

- trwatkins1

oh yea

- e.mccormick

Remember how the absolute value works.

- trwatkins1

so 7

- 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

IF it had been |y| < 6, it would have been the other two. But for |y| > 6 it is A and D.

- e.mccormick

I hope that makes more sense now.

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