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The 2 absolute equation equality? find the max and min of x?

  1. Jun 20, 2017 #1
    1. The problem statement, all variables and given/known data
    15_Mat_B_-_1.6.png

    2. Relevant equations


    3. The attempt at a solution
    2x - 1 >= 0
    x >= 1/2

    x - 2 >= 0
    x >= 2

    for x <1/2
    then 2x - 1 and x - 2 are negative
    solve : -(2x-1) - (x-2) = 2
    -3x + 3 = 2
    x = 1/3

    for 1/2 <= x < 2
    the (2x - 1) positive, (x-2) negative
    solve : 2x -1 -x + 2 = 2
    x = 1

    for x>= 2
    both 2x -1 and x -2 = positive
    2x - 1 + x - 2 = 2
    3x = 5
    x = 5/3

    is my answer right? then the max of x is 5/3? and the min is 1/3?
     
  2. jcsd
  3. Jun 20, 2017 #2

    Mark44

    Staff: Mentor

    These are the values I get, as well.
     
  4. Jun 20, 2017 #3
    so what's the max and min of x? because the key answer not 1/3 and 5/3. but 1/3 and 1
     
  5. Jun 20, 2017 #4
    Your third case is self-contradictory. On the assumption that x >= 2, you get x = 5/3, which is < 2. So this case is ruled out, and the answers are 1/3 and 1.
     
  6. Jun 20, 2017 #5

    Mark44

    Staff: Mentor

    Yes, @mjc123 is correct. I wasn't careful enough in checking my solutions. The maximum value is x = 1.
     
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