Results 1 to 3 of 3

Thread: Graphing Absolute Value Inequality: 9|x - 2| - 10 >= -64

  1. #1
    New Member
    Join Date
    Aug 2017
    Posts
    3

    Graphing Absolute Value Inequality: 9|x - 2| - 10 >= -64

    I have a question. What's the answer to 9|x-2|-10>=-64? I thought it was all real numbers, but my teacher said it was no solution since absolute value can't equal a negative. Thanks in advance.

  2. #2
    Elite Member mmm4444bot's Avatar
    Join Date
    Oct 2005
    Location
    AZ, Seattle, San Diego
    Posts
    9,839
    Quote Originally Posted by jennie View Post
    What's the [solution for] 9|x-2| - 10 >= -64 ?

    I thought it was all real numbers, but my teacher said it was no solution since absolute value can't equal a negative.
    I agree with your solution; your teacher might have been thinking about a different situation.

    The inequality symbol ≥ means greater than OR equal.

    As long as the left-hand side evaluates to a number that is greater than -64, the inequality is true. This happens for any value of x.

    If you solved the inequality by hand, you ought to have reached this:

    |x - 2| ≥ -6

    This shows that x can be any Real number because |x-2| is non-negative, and any non-negative number is greater than -6.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  3. #3
    Elite Member mmm4444bot's Avatar
    Join Date
    Oct 2005
    Location
    AZ, Seattle, San Diego
    Posts
    9,839
    Graphing each side of the given inequality is another way to solve it.

    The graph of the left-hand side (green) lies entirely above the graph of the right-hand side (red).

    In other words, at each value of x, the value of y on the green graph is greater than the value of y on the red graph.
    Attached Images Attached Images
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •