Question

solve: |x=6|-4=2

Answer 1

|x+6|-4=2

Answer 2

abs(x+6)=2+4=6
abs(x+6)=6
x+6=6 and x+6=-6
x=0 x=-12

Answer 3

example:
abs(x)=6
what two values for x will give you distance 6 do you know?

Answer 4

x+6 = 0 --> x=-6
-x-6 = 0 ---> x=-6

Answer 5

how far is -6 away from 0?
how far is 6 away from 0?

Answer 6

they are both six units from 0

Answer 7

abs(x)=6 has two solutions
x=6 and x=-6
just like we found 2 solutions above
but these problems could get trickier along the way and sometimes it will fail to have two solutions
so you should begin checking to get in the practice of doing so

Answer 8

so let's check the above one:
we got x=0 and x=-12
lets see if x=0 works
plug it into the original equation
abs(0+6)-4=2
abs(6)-4=2
6-4=2
2=2
so we got the samething on both sides so x=0 checks out
how about x=-12
abs(-12+6)-4=2
abs(-6)-4=2
6-4=2
2=2
so x=-12 checks out

Answer 9

any questions?

Answer 10

OK! That makes perfect sense once you broke it down for me!! Thank you both so very much :)

Answer 11

u r welcome

Answer 12

Really it's simply a matter of:
\[|x+6| - 4 = 2 \implies |x+6| =6 \]\[\implies x + 6 = 6 \text{ and } x+ 6 = -6\]
\[\implies x = 12 \text{ and } x = 0\]
are solutions.

Answer 13

no polpak i already won

Answer 14

lol

Answer 15

lol. I have another one similar to that, think you could help? \[3x-1\le 7\]

Answer 16

and he meant x=-12 not 12

Answer 17

Yes, whoops.

Answer 18

Certainly, though this one doesn't involve absolute values.

Answer 19

add the 1 to both sides

Answer 20

what do you get after you do that?

Answer 21

\[3x \le8\]

Answer 22

and when you divide both sides by 3?

Answer 23

omg gj

Answer 24

3/3=1
so 3x/3=x
so we have
x<=8/3

Answer 25

good...got the same answer!!! Thanks.