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Inequality intersection help

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]|2x-1|+|x+2|\geq 4x[/tex]


    2. Relevant equations



    3. The attempt at a solution

    For x<-2 , [tex]-(2x-1)-(x+2)\geq 4x[/tex]

    [tex]x\leq -\frac{1}{7}[/tex]

    For [tex]x\geq \frac{1}{2}[/tex]

    [tex]2x-1+x+2\geq 4x[/tex]

    [tex]x\leq 1[/tex]

    For [tex]-2 \leq x < \frac{1}{2}[/tex] ,

    [tex]-(2x-1)+x+2\geq 4x [/tex]

    [tex]x\leq \frac{3}{5}[/tex]

    after combining , the solution would be [tex]x\leq -\frac{1}{7} [/tex]

    AM i correct ? but the answer given is [tex]x\leq 1[/tex]
     
  2. jcsd
  3. Mar 9, 2010 #2

    tiny-tim

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    Homework Helper

    Hi thereddevils! :wink:

    Your three answers are correct, but you're not putting them together correctly.

    For example, you have:

    if x ≤ -2, it's true for x ≤ -1/7.

    so it's true for all x ≤ -2.

    ok, now try the others. :smile:
     
  4. Mar 9, 2010 #3
    Re: inequality

    thanks tiny , yeah , i am confused with the last part , what i did is to put x<= -1/7 , x<=1 , x<= 3/5 on the number line and take the intersection which is what i got .

    so say for x>= 1/2 , x can be 4 , x<=1 , so 4<=1 ?? this is not true

    i am sorry , i still do not understand the last part .
     
  5. Mar 9, 2010 #4

    tiny-tim

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    There are three possibilities:

    x ≤ -2, -2 ≤ x ≤ 1/2, 1/2 ≤ x.

    call them A B and C.

    So A or B or C.

    If A, the equation is true if (say) a.

    If B, the equation is true if (say) b.

    If C, the equation is true if (say) c.

    So the equation is true if (A and a) or (B and b) or (C and c). :wink:
     
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