Question

Solve |x| < 5
{x|-5 < x < 5}
{x|x < -5 or x > 5}
{-5, 5}

Answer 1

Hi countrygirl1431,
Think of absolute value as *distance from zero*.
So, you 're being asked for all the (real numbers, presume) whose *distance from zero is less than 5". Think of shading those on a number line; remember, you can move less than five units to the right ... or, less than five units to the left... what numbers do you get? Can you report it in interval notation?
This web page of mine might be useful:
http://www.onemathematicalcat.org/algebra_book/online_problems/solve_abs_val_ineq_lt.htm

Answer 2

Your first line was good:
|x| < 5 means you want { x | -5 < x < 5 }
But from there, you got off a bit...
-5 < x < 5 means "-5 < x AND x < 5" ...
so, you want all the numbers greater than -5 *and at the same time* less than 5...

Answer 3

im confused

Answer 4

Okay ... think of it this way. You're standing at the number "0" on a number line.
I tell you: you can move away from this number, but not too far ... you can only travel less than 5 away from here. Can you get to the number 3? Can you get to the number -3?
Can to you get to 4.9? How about 5.1?

Answer 5

(Do you know interval notation ... it uses parentheses when endpoints aren't included, and brackets when endpoints are included ... it will be useful to you to report your anwer!)

Answer 6

you cant get to 5.1

Answer 7

This is a much better page for you than the one I posted before (sorry); it has only really simple absolute value sentences... maybe it will help you..
http://www.onemathematicalcat.org/algebra_book/online_problems/solve_simple_abs_val_sen.htm

Answer 8

Right!!! But you CAN get to all the others I listed. Can you get to -4.99? Can you get to -5.01?

Answer 9

ok thanks

Answer 10

So .... can you tell me all the numbers with |x| < 5, using interval notation?

Answer 11

no im still really confused

Answer 12

We can figure this out together --- don't despair! Absolute value is hard for LOTS of people. Let's go back to basics ... do you understand that |x| means "the distance x is from 0 on a number line" ?

Answer 13

Since 5 is 5 units from 0, |5| = 5.
Since -5 is also 5 units from 0, |-5| = 5 also.

Answer 14

ok i got that much

Answer 15

Good. Then think of "|x| < 5" as a question. I'm asking you:
I want all the numbers x, whose distance from zero is LESS THEN 5.
Does that part make sense?

Answer 16

Whenever my students see those absolute value bars, I like to have them take their hand and do "karate chops" on the bars: saying "distance from zero"!

Answer 17

If you stand at zero, and I ask you to walk away exactly five units ... where can you get to? (Remember --- you can walk in two directions.)

Answer 18

so the numbers between 5 and -5 would be -4, -3, -2, -1, 0, 1, 2, 3, 4

Answer 19

You're getting close!!! Those are all the *integers* between -5 and 5 ... yes! But, what about 1/2? What about -4.9?

Answer 20

You certainly can't list them all... right? That's why we need *interval notation* to come to the rescue!

Answer 21

You can search for "interval notation" on this page, if you need a review:
http://www.onemathematicalcat.org/algebra_book/online_problems/introduction_to_sets.htm#intervalNotation

Answer 22

I've got to get going ... but hope this has helped. Have a great day!

Answer 23

thanks