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countrygirl1431

  • one year ago

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

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  1. anonymous
    • one year ago
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    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

  2. anonymous
    • one year ago
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    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...

  3. countrygirl1431
    • one year ago
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    im confused

  4. anonymous
    • one year ago
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    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?

  5. anonymous
    • one year ago
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    (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!)

  6. countrygirl1431
    • one year ago
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    you cant get to 5.1

  7. anonymous
    • one year ago
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    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

  8. anonymous
    • one year ago
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    Right!!! But you CAN get to all the others I listed. Can you get to -4.99? Can you get to -5.01?

  9. countrygirl1431
    • one year ago
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    ok thanks

  10. anonymous
    • one year ago
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    So .... can you tell me all the numbers with |x| < 5, using interval notation?

  11. countrygirl1431
    • one year ago
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    no im still really confused

  12. anonymous
    • one year ago
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    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" ?

  13. anonymous
    • one year ago
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    Since 5 is 5 units from 0, |5| = 5. Since -5 is also 5 units from 0, |-5| = 5 also.

  14. countrygirl1431
    • one year ago
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    ok i got that much

  15. anonymous
    • one year ago
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    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?

  16. anonymous
    • one year ago
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    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"!

  17. anonymous
    • one year ago
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    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.)

  18. countrygirl1431
    • one year ago
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    so the numbers between 5 and -5 would be -4, -3, -2, -1, 0, 1, 2, 3, 4

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

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

  21. anonymous
    • one year ago
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    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

  22. anonymous
    • one year ago
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    I've got to get going ... but hope this has helped. Have a great day!

  23. countrygirl1431
    • one year ago
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    thanks

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