## anonymous 5 years ago solve: |x=6|-4=2

1. anonymous

|x+6|-4=2

2. myininaya

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

3. myininaya

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

4. anonymous

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

5. myininaya

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

6. myininaya

they are both six units from 0

7. myininaya

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

8. myininaya

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

9. myininaya

any questions?

10. anonymous

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

11. myininaya

u r welcome

12. anonymous

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.

13. myininaya

14. myininaya

lol

15. anonymous

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

16. myininaya

and he meant x=-12 not 12

17. anonymous

Yes, whoops.

18. anonymous

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

19. myininaya

add the 1 to both sides

20. myininaya

what do you get after you do that?

21. anonymous

$3x \le8$

22. anonymous

and when you divide both sides by 3?

23. myininaya

omg gj

24. myininaya

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

25. anonymous