Question

Match each absolute value sentence with its solution set.

Potential Matches:
(1) {x|x > 4 or x < -4/5}
(2) x < -1/3 or x > 1
(3) {4/3, -4}
(4) {x| -11 < x < -7}
(5) no solution

Answer
A :
|x + 9| < 2
B:
|5x - 8| > 12
C :
|3k + 4| = 8
D :
|x - 6| = -10
E :
|-6x + 2| > 4

Answer 1

do you know what absolute sign is ? and what is its effect ?
like what is |-4| =... ?

Answer 2

either -4 or 4

Answer 3

no, its just 4
because |....| makes a negative number , positive.
|-a| = a (if a>0)
|-a| =-a (if a<0)
got this ?

Answer 4

uhh.. no.
I got you up until you added the last line.

Answer 5

|-a| =-a (if a<0)
this ?
let a=-1
then
|-(-1)|= -(-1)=1
ok?

Answer 6

okay..

Answer 7

so, basically |....| can never be negative.
if you find something like |.....| =-10
then there will be no solution to this.

Answer 8

Okay. This is making a little more sense to me. Can you tell me how to actually figure one out though? Preferably one with a < or > sign?

Answer 9

yes, i gave you that so that you can solve D.
when
\(|x|>a \implies x>a , \: x<-a \\or, -a<x<a\)
similarly,
\(|x|<a \implies x<a , \: x>-a \\or, -a>x>a\)
so, what about
\(|x+9|<2\)
?

Answer 10

{x| -11 < x < -7}??

Answer 11

just a second, i messed up with signs,sorry...
yes, i gave you that so that you can solve D.
when
\(|x|>a \implies x>a , \: x<-a \\or, -a>x>a\)
similarly,
\(|x|<a \implies x<a , \: x>-a \\or, -a<x<a\)
so, what about
|x+9|<2
?
and yes, that is correct.!

Answer 12

A4
B1
C3
D5
E2

Would these be right?

Answer 13

for \(|x|=a \implies x=a, x=-a\)
so, for |3k + 4| = 8,
you get (3k+4)=8, (3k+4)=-8
can you solve these two normal equations to get 2 values of 'x' ?

Answer 14

yes, those are correct!
are you sure you got them after understanding the whole thing ??
ask if you have any sort of doubts....

Answer 15

Yea I get it now. I have exams in a week and I'm studying and I couldn't remember how to do these to save my life! Thank you so much!

Answer 16

ok, welcome ^_^