Question

-2|x-14|+16
11 years ago

Answer 1

\(-2|x-14|+16\le 6\) ?

Answer 2

yes

Answer 3

9 and 19 are involved, but are you saying it is the range between and including them?

Answer 4

See, I am wondering if you flipped the inequality when you did the divide by -2.

Answer 5

I did

Answer 6

oh wait no i didn't

Answer 7

Kk. Yah, that would make the difference I see in answers.

Answer 8

how would that change the answer?

Answer 9

\(-2|x-14|+16\le 6\)

\(-2|x-14|+16-16\le 6-16\)

\(-2|x-14|\le -10\)

\(-2|x-14|/-2\ge -10/-2\)

\(|x-14|\ge 5\)

Well, it would make it very different from that point on.

Answer 10

I'm sorry I'm still not seeing it

Answer 11

Well, do you know what step is next at that point?

Answer 12

x-14>15
x-14<-15

Answer 13

with lines under the ><

Answer 14

5 not 15

Answer 15

\(x-14\ge 5\)
and
\(x-14\le -5\)

OK. That is one way of saying it. Another is:
\(-5 \ge x-14 \ge 5\)

They end up the same in the end.

\(x-14+14\ge 5+14\)
and
\(x-14+14\le -5+14\)

\(x\ge 19\)
and
\(x\le 9\)

OK, do you see a difference yet?

Answer 16

See, your answer, as I read (9, 19), means anything above 9 that is also below 19.

Answer 17

so it should be (19, 9)? I'm sorry I'm so bad at this

Answer 18

no thats wrong

Answer 19

OK, so your calculations were the same as mine, basically, and the difference is in the end answer? Just trying to see where the problem is.

Are you doing the answer in interval notation?

Answer 20

yea

Answer 21

OK. Interval notation basics:

(a,b) means from a to b, but not including a or b.
[a,b] means from a to be inclusive
[a,b) means from a, including a, to b but not b.

Then there is the \(\cup\) or union to join things. It is sort of like saying OR

[a,b)\(\cup\)(c,d) means from a, including a, to b but not b OR from c to d, but not including c or d.

Are you using that stuff?

Answer 22

I didn't in my answer because when I did it said i had overlapping intervals

Answer 23

OK. Well, \(x \le 9\) and \(x \ge 19\) means anything below 9, including 9 is fine. Between 9 and 19 is bad. Above 19 and including 19 is also fine.

btw: I just type in the \(\LaTeX\) for the calculations: `\(x \le 9\)` and `\(x \ge 19\)`

Answer 24

i dont know what that means

Answer 25

Which, the \(\LaTeX\) or the description of the answers?

Answer 26

both

Answer 27

Well, the \(\LaTeX\) just lets me make pretty math: \(\int\limits_5^x\dfrac{x^9-\cos x}{\sin x}\)

The description... hmmm.... it means this:

https://www.desmos.com/calculator/dneci7e14f

That is what it would look like on a number line. See the gap from 9 to 19?

Answer 28

yea

Answer 29

Well, if you are doing interval notation, you need a union to show that. The union between the left part of the answer (9 and below) and the right (19 and above).

Answer 30

so (-inf, 9) U (19, inf)

Answer 31

Almost! There is one small difference. The equals part of \(\le\) and \(\ge\) makes the 9 and 19 included.

\((-\infty,9]\cup [19,\infty)\)

See how I use d ] U [ in the middle? That is the inclusive part.

Answer 32

Okay I think I get it now thanks so much (:

Answer 33

Just FYI, your original answer of (9, 19) means 9<x<19

Answer 34

So you can see why I thought it was the - not flipping things to make it:
\(9 \ge x \ge 19\)

Answer 35

Which is poor notation, but I think it gets the point across.

Answer 36

Better notation would be \(9\ge x, x \ge 19\) The comma meaning and/or.

Answer 37

Well, I am off. I hope that helps. And for the heck of it, you can turn on and off the three things in this one by clicking on the colored dots on the left:

https://www.desmos.com/calculator/8wdkhxshcz

The blue is your original question.
The red is the original, wrong answer.
The black is the corrected answer.