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Homework Help: Absolute graphs

  1. May 22, 2010 #1
    1. The problem statement, all variables and given/known data

    Sketch the graph of y = 2|x - 1| - 3|x + 1| + 3x + 1, and hence solve the inequality 2|x - 1| - 3|x + 1| + 3x + 1 < 0

    2. Relevant equations

    None

    3. The attempt at a solution

    (Refer to attachment).

    I dont know where (or if) I made a mistake, cause when I try drawing the graph, it looks nothing like the answer.
     
  2. jcsd
  3. May 22, 2010 #2

    try to consider when x=2 , x=0.5, x=-2 and see what happen
     
  4. May 22, 2010 #3
    To generalize, think of the PIECEWISE defined function.
    |x-1| is defined differently "to the left of x = 1" than it is "to the right of x = 1".
    |x+1| ................................. x = -1

    So when x is less than -1, |x+1| = -(x+1) and |x-1| = -(x-1).
    If you don't understand the previous sentence, review the definition of the absolute value function and piecewise functions.

    Having discussed what happens when x < -1, now let's consider when x is greater than or equal to -1. "Things change" (i.e. the piecewise abs definitions) when x = 1, so let's consider the interval [-1, 1).
    On this interval, |x-1| = -(x-1) and |x+1| = (x+1).

    What happens on [1, inf) ??
     
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