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

Question

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

smokeysthename · Answer

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

realitywillslapyou · Answer

Solve and graph the absolute value inequality: |2x + 4| > 14

smokeysthename · Answer

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

smokeysthename · Answer

do you see how i did that?

realitywillslapyou · Answer

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

realitywillslapyou · Answer

I am so bad at math

smokeysthename · Answer

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

realitywillslapyou · Answer

Okay, (•-•;*)

smokeysthename · Answer

do you want my help?

realitywillslapyou · Answer

Yes please

smokeysthename · Answer

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

realitywillslapyou · Answer

Okay

smokeysthename · Answer

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

smokeysthename · Answer

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

realitywillslapyou · Answer

x ≥ 4?

smokeysthename · Answer

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 · Answer

x ≤ -(11/2)?

smokeysthename · Answer

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

realitywillslapyou · Answer

x ≤ -(5.5/1)?

smokeysthename · Answer

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 · Answer

No....

smokeysthename · Answer

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 · Answer

do you understand why now* i should say

realitywillslapyou · Answer

Yeah, I think so

smokeysthename · Answer

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

realitywillslapyou · Answer

What about the question with the attachments?

realitywillslapyou · Answer

I think it's "a"

smokeysthename · Answer

just one sec . lemme do it first

smokeysthename · Answer

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

realitywillslapyou · Answer

Thank you! :D

smokeysthename · Answer

no problem (: