Solve the absolute value inequality: |4x + 3| ≥ 19
A) x ≤ -5.5 and x ≥ 4
B) x ≥ -5.5 or x ≤ 4
C) x ≤ -5.5 or x ≥ 5.5
D) x ≤ -5.5 or x ≥ 4

- RealityWillSlapYou

- jamiebookeater

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- SmokeysTheName

since there is an absolute value sign you have to set up 2 equations.

- SmokeysTheName

one that says: |4x + 3| ≥ 19
and one that says: |4x + 3| (lessthan / equal to) - 19

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## More answers

- SmokeysTheName

do you see how i did that?

- RealityWillSlapYou

I just need to know which one I chose.... I'm on a time crunch

- RealityWillSlapYou

I am so bad at math

- SmokeysTheName

im not going to just give you the answer. i will help you understand it tho..

- RealityWillSlapYou

Okay, (•-•;*)

- SmokeysTheName

do you want my help?

- RealityWillSlapYou

Yes please

- SmokeysTheName

|dw:1359407665618:dw|okay so you will set them up like this:

- RealityWillSlapYou

Okay

- SmokeysTheName

you have to set up 2 equations because there is an absolute value sign

- SmokeysTheName

after that you solve for x. so start with the positive 19 equation
when you solve for x what will you get.

- RealityWillSlapYou

x ≥ 4?

- SmokeysTheName

yes, now you got that one.. so just by looking at the answers you know its either a/d
now do the second equation. what do you get?

- RealityWillSlapYou

x ≤ -(11/2)?

- SmokeysTheName

thats not all the way simplified but you're close , that simplifies down to ?

- RealityWillSlapYou

x ≤ -(5.5/1)?

- SmokeysTheName

yes which is also just -5.5
okay and so now you definitely know its either a/d
okay the difference between a and d is that the middle word in a is "and" and the middle word in "d" is or.. do you know the difference between those?

- RealityWillSlapYou

No....

- SmokeysTheName

okay since you had the absolute value sign i told you before that you had to make two equations. and when you have to make two equations that means both of those answers need to be "included" so it would be "and". do you understand why?

- SmokeysTheName

do you understand why now* i should say

- RealityWillSlapYou

Yeah, I think so

- SmokeysTheName

okay good ! so your answer is a. good work (:

- RealityWillSlapYou

What about the question with the attachments?

- RealityWillSlapYou

I think it's "a"

- SmokeysTheName

just one sec . lemme do it first

- SmokeysTheName

yess you are correct!! (: good job (:

- RealityWillSlapYou

Thank you! :D

- SmokeysTheName

no problem (:

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