Question

HELP???

Which answer is the solution to the inequality |x|<3?

A) x>-3 or x<3

B) x<-3 or x>3

C) x<-3 and x<3

D) x>-3 and x<3

I can't figure this one out :/ can someone explain

Answer 1

Do you know about absolute values?

Answer 2

@compassionate I am learning about them right now, I seem to understand how to find a solution set of a compound inequality, but this question seems so hard and I don't understand how to get the correct answer.

Answer 3

Imagine a number line. And on that line we have points from 10 to -10.

Say I am being asked to graph |x| < 3

This is saying, all the numbers that are LESS THAN 3 away from 0 in either direct.

The number 1 will work, as will –1; the number 2 will work, as will –2. But 4 will not work, and neither will –4, because they are too far away. Even 3 and –3 won't work (though they're right on the edge). But 2.99 will work, as will –2.99. In other words, all the points between –3 and 3, but not actually including –3 or 3, will work in this inequality.

So which one do you think represents less than 3 and -3 but not actually 3 and -3

Answer 4

@compassionate it's the distance from the number line correct? So I think it's x<-3 or x>3 (B) that one also because it's "or" and when you graph them they aren't overlapping so it is an disjunction. I over thought it I guess

Answer 5

Correct