Question

Hi everyone! Can someone tell me why my teacher did this: |x-9|<1 so then -1 13 years ago

Answer 1

is it because the limit of |x-9| as "n" goes to infinity is simply |x-9|? I just don't see why you just drop the absolute value signs once you put it into an inequality?

Answer 2

what do you know when you have something in absolute?

Answer 3

i mean..what is the definition of the absolute value?

Answer 4

because for term in absolut is x-9, not x+9 :)

Answer 5

the solution of ineq :
|f(x)| < c, (with c positive) is
-c < f(x) < c

Answer 6

\[\left| x-9 \right|=\]
x-9 if x>0
-(x-9) if x<0

for those 2 solutions if you put them into your equations you will get x<10 and x>8

Answer 7

sorry x-9 if x-9>0 and -(x-9) if x-9<0

Answer 8

not sure i follow you...any chance you can answer why he removed the absolute value sign but left it x-9 instead of changing it to x+9 using english rather than math examples? I just need the intuition here why it wasn't changed to x+9...thanks

Answer 9

let k = x-9

|k| < 1, implies that: -1 < k < 1

since k = x-9; -1 < x-9 < 1


you appear to be confusing the value of (x-9) with the visual clue that an absolute value suggests.

an absolute value function does not turn all subtraction signs into addition signs ....

Answer 10

ok...i get it now! thanks everyone!

Answer 11

:) good luck