Question

What is the solution set of |2x + 4| < 12?


What is the solution set of |4x – 3| – 1 > 12?


What is the solution set of |x – 6| = 4?

Answer 1

|f(x)| < p
=>
-p < f(x) < p

Answer 2

can you do it now ?

Answer 3

Okay, let's start with:
|x – 6| = 4

What are the two possible scenarios that you're going to have to solve to find x?

Answer 4

add 6 on both sides?

Answer 5

No, the absolute value is already isolated.

Answer 6

|f(x)| = p
=>
f(x) = p , f(x) = -p

Answer 7

i honestly dont understand that @Coolsector :/

Answer 8

whats F=?

Answer 9

|x – 6| = 4
let x-6 = f(x)
4 = p
so
|f(x)| = p
mean two options
f(x) = p , f(x) = -p

Answer 10

it think you get
x-6 = -4
x-6 = 4
always remember that in sums having mode there is never one answer
you get two or range of answers

Answer 11

You'll want to remove the absolute value bars by writing two equations:
x-6 = 4 (this one you get just by dropping the bars)
x-6 = -4 (and the negative case.)

Answer 12

Ok so whenever the absolute value is already isolated , you make an equation out of them to get your anwsers?

Answer 13

yes............now try to solve first one

Answer 14

Yeah, just drop the bars for the first case, and then for the second case, switch the signs if you're dealing with an inequality (you're not here) and make it negative.

Answer 15

okay, so would x=10?

Answer 16

Yes, so now for the second one.

Answer 17

-10?

Answer 18

x-6 = -4
+6 +6

x = 2

Answer 19

okay i see how you got that where the <12 come into play?

Answer 20

when |f(x)|<12
then -12<f(x)<12
try to use this

Answer 21

Okay, now let's go through the first problem:
|2x + 4| < 12
This one is slightly different.

When you create your first of the two scenarios, you're going to just drop the absolute value bars. So, what's the first scenario?

Answer 22

2x=4<12

Answer 23

2x + 4 < 12

For the second scenario, you're going to switch the inequality sign AND make the 12 negative. So what's the second scenario?

Answer 24

2x=4<-12

Answer 25

You have to switch to inequality sign, so what once what < is now >.

Answer 26

so it would be" 2x=4>-12

Answer 27

-12<2x+4<12
sub -4 from both sides
-16<2x<8
divide both sides with 2
-8<x<4

Answer 28

Yep, but you've got an = where a + should be.
Now solve both scenarios.

Answer 29

@melbel
is it correct?

Answer 30

opps lol my bad! 2x+4=>-12

Answer 31

Yeah, uzumakhi, you got it.
So what did you get, @CIERA1338, when you solved each scenario. (I keep calling them scenarios. What are they really called @uzumakhi?)

Answer 32

i get how @uzumakhi worked it previously but y does he flipped the equation?

Answer 33

okay just noticed he didnt flip it lol he subtracted the 12< from both sides right to get rid of it?

Answer 34

i dont know what they really call it but i know how to use it

Answer 35

i really dont know

Answer 36

-8<x<4 is what i would come out with in the end after dividing 2 into both sides

Answer 37

check your answer..........i also got the same

Answer 38

That's what I got.

Answer 39

so only second part is left

Answer 40

So what is the first step in solving this one:
|4x – 3| – 1 > 12

Answer 41

you gotta get the |4x-3| by itself right?

Answer 42

|4x-3| -1 > 12
|4x-3| > 11
so we have two conditions
|4x-3| > 11
|4x-3| > -11

Answer 43

Yep!

Answer 44

|4x-3>11
|4x-3|>-11

Answer 45

these are the 2 scenarios right? @melbel

Answer 46

4x>14
x>14/4

Answer 47

1. |4x-3|>11
2 . |4x-3|>-11

Yep, but remember in the second scenario (the negative case) to flip the inequality sign when you drop the absolute value bars. So drop ur bars. :P

Answer 48

1.) 4x-3>11

2.) 4x-3<-11

Answer 49

Yep!

Answer 50

yay! now i subtract 3 from both sides and 4x>8 for the first on right??

Answer 51

Well, this time you'll add three to both sides (since it's negative)

Answer 52

1.) 4x-3>11
+3 +3

(so that you can knock out that -3 on that one side)

So you'll get
4x>14 for the first one (so far, anyway.)

Answer 53

4x>14
4x<-14

Answer 54

yes, i got the first one would the second one be the same or no?

Answer 55

Careful on the second one:
2.) 4x-3<-11
You're adding a positive 3 to a -11
So it'll be -8
4x<-8

I do the same thing all the time, lol!

Answer 56

opps!

Answer 57

1.) 4x>14
2.) 4x<-8

Now we have to get x by itself for each of the scenarios.

Answer 58

the first one kind of sucks, you have
(4x>14)/4
x>14/4
simplify the fraction
x>7/2 (I hate fractions.)

Answer 59

so you'd get like 2.5

Answer 60

The second one is nicer:
4x<-8
x<-2

Answer 61

3.5 and it depends whether or not your teacher allows decimals. Mine punishes us with fractions, so I would have to leave it at x>7/2

Answer 62

x>7/2
x>3.5 not 2.5

Answer 63

i was just going by my anwser chioces lol x > –2.5 or x > 4

x < –2.5 or x > 4

x < 2.5 or x > 4

x < –4 or x > 4

Answer 64

what would i get as the anwser?