math

posted by .

absolute value of(x + 3) + absolute value of (3 - x) < 9.

I am not sure how to go about this question. Although, we generally use three cases.

  • math -

    let's rewrite it as
    |x+3| < 9 - |3-x|
    x+3 < 9 - |3-x| or -x-3 < 9 - |3-x|
    |3-x| < 6-x , #1)
    or
    |3-x| < 12 + x , (#2)

    from #1
    3-x < 6-x
    no solution
    or
    -3 + x < 6-x
    2x < 9
    x < 9/2

    from #2
    3-x < 12+x
    -2x < 9
    x > -9/2
    or
    -3+x < 12 +x
    no solution

    so we have x< 9/2 and x > -9/2

    our critical values of -9/2 and +9/2 divide our number line into 3 parts
    1. x < -9/s
    2. x between -9/2 and 9/2
    3. x > 9/2

    I usually pick an arbitrary number in each region and test it in the original

    1. let x = -10 --> |-7|< 9 -|13| false
    2. let x = 0 ---> |3| < 9 - |3| true
    3. let x = 10 --> |13| < 9 - |-7| false

    so -9/2 < x < 9/2

  • math -

    Thank You!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    i can figure this out -2+|-5+6| i try inverse but im still getting it wrong ive been stuck on this fo awhile There is no inverse in the equation. the |...| means absolute value. We perform what is indicated in the |,,| and that is …
  2. math, help

    For the following set, which number has the largest absolute value?
  3. math

    when in the absolute value of x equal to the absolute value of negative x?
  4. math !!!!!!please part of a major grade!!!!!!

    when in the absolute value of x equal to the absolute value of negative x?
  5. Math

    I'm having trouble on the 2nd part of the question below. The value of a 1962 Mickey Mantle baseball card went from $900 to $700. a. Write an integer to describe the change in value in the card. ( I know this would be -200) b. Use …
  6. Calculus

    Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =
  7. Calculus

    Find the absolute extrema of the function. (Round your answer to three decimal places.) f(x) = xe^-x2 on [0,2] Absolute maximum value: at x = Absolute minimum value: at x =
  8. Math

    1. Suppose a and b are integers, and the absolute value of a is > than the absolute value of b. Must a be greater than b?
  9. algebra

    How many cases would there be for an absolute value with 3 sets of absolute value symbols?
  10. Math(Calculus)

    Im having a real difficult time solving this question. Find the absolute extrema of the function. h(x) = e^x^(2) - 4 on [-2,2] Absolute maximum value: at x = Absolute minimum value: at x =

More Similar Questions