Question

What is the solution set of the absolute value sentence
|6x + 8| > -4?

A. {4/3, -4}
B. {x|x > 4 or x < -4/5}
C. No Solution
D. {x|-11 < x < -7}
E. All Real Numbers

Answer 1

ok.

Answer 2

Even better...here's the trick. An absolute value is always positive...and your asking when will that number be greater than *negative* 4...

Answer 3

Can a positive number ever be less than -4?

Answer 4

Of course, when I say positive, I also am including 0...although 0 is neither positive nor negative.

Answer 5

how come i got ]-2/3;-2[

Answer 6

? hmmm

Answer 7

Can a positive (or zero) ever be less than -4?

Answer 8

yes

Answer 9

@angela - if you do work on this problem it will lead you weird. Just look at what the question is asking.

Answer 10

@lisa - how can a positive number be smaller than a negative number?

Answer 11

expression on the left is absolute value. expression on the right is less than zero. do not try to solve using algebra

Answer 12

OH SRY!!

Answer 13

:) s'ok...since as @satellite said, the expression on the right is an absolute value, it is *always* going to be either 0 or positive...and therefore *always* > -4.

So what is the answer?

Answer 14

x>-2, x<-2/3

Answer 15

im still kinda confused

Answer 16

FIrst, you understand that 0>-4.

Now, whatever 6x+8 equals, when you take it's absolute value, it is going to be positive. So for all real numbers, x, that you choose,\[\left| 6x+8 \right|\ge0>-4\]

Answer 17

So no matter what we choose for x, the inequality holds true.

Better?

Answer 18

@jeremy - don't try using algebraic methods...it won't work.

Answer 19

Okay so basically how you have to do it is through the following steps. First do 6x+8>-4, subtract 8 from each side and you get 6x>-12. Now divide each side by six and you get x>-2. Now for the second solution (which all inequalities have), multiply (6x+8) times -1. Then you get -6x-8>-4. Add eight to each side and you get -6x>4. Then divide each side by -6 and you switch the inequality sign and get x<-2/3. So the two solutions are x>-2, and x<-2/3

Answer 20

That's incorrect jeremy.

Answer 21

@jeremy - look at @satellite's post

Answer 22

so it would be E

Answer 23

Very good @lisa. Do you understand why?

Answer 24

Oh you're right. It would obviously be all real numbers because anything in the absolute value bar is positive. Therefore every number because positive numbers are obviously greater than -4

Answer 25

I POSTED ANOTHER QUESTION LIKE IT... AM I RIGHT?

Answer 26

You now have a third "tool" to use to solve these. The two I gave you earlier on translating the inequalities...and now,

An absolute value greater than a negative numebr is true "for all real numbers."

Math is all about learning tools that help you solve the problem.

Answer 27

Let me look at it and see. :)

Answer 28

thnx guys :)