Question

Please help me!!

http://i.imgur.com/eQkl89E.jpg
Solve the inequality and graph the solution on the real line.

Answer 1

|x-a|<b
implies
-b<x-a<b

Answer 2

how did you get that? can you explain D:

Answer 3

@zzr0ck3r >_< sorry, but i really want to know how to figure this out ;-;

Answer 4

I'm not exactly sure how to explain where it comes from, but I can prove it with an example.
Let's just pick some numbers for a and b. I'll say |x-2|<3
Now as zz said, this implies
-3 < x-2 < 3
When you have a problem like this, you want x by itself, which is done by adding 2 to all 3 portions of the inequality, giving us
-1 < x < 5
Now let's just check this interval range. So the lowest number that works is any number above -1. Well, if I plugged -0.9 for example:
|-0.9 - 2|<3
|-2.9| = 2.9 < 3
So we see that works. The largest number in that range was 5. So let's just try 4.9
|4.9-2|<3
|2.9|<3
|2.9| = 2.9, so that works, too. This interval definitely appears to work. I wish I hadsome perfect definitional reasoning, but if you see
|x| < y where the absolute value is less than some quantity, it means you need to set it up like
-y < x < y

Answer 5

okay, thank you. ; v ;

Answer 6

@ineptAtMath
Its a bit different if the inequality is facing the other way, though. Do you know how you would set that up?

Answer 7

no, not really. :< i just don't get it with variables for some reason. :<

Answer 8

Alright. Well this is the set up if its the other way

Answer 9

If:
\[|x| > a\]then
\[x < -a \]and
\[x > a \]
So in this pattern, basically x is less than the low, higher than the high. Which is how I think of it. Greater than positve a, lesser than negative a.
So an example would be something like
|x-1| > 1 This means I need to separate inequalities. Less than the less, higher than the high.
x-1 < -1
x -1 > 1
This means: x < 0 and x > 2
So this means x is all numbers not between 0 and 2. So let's test the numbers in that range to check:
|0.1-1| > 1
|-.09| > 1
.09 > 1 So you can see that having a number inside of 0 doesnt work. Now a number inside of 2
|1.9-1|>1
|.9|>1
.9 >1. Again not true. But of course if we go any number less than 0 or greater than 2 itll work for sure
|-1 - 1| > 1
|-2| > 1
2 > 1 check
|3-1| > 1
|2| > 1
2 > 1 check. So you can see how this interpretation works when we have the absolute value greater than the quantity.

Answer 10

Thank you again. :)

Answer 11

Yeah, np :3