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Kayasari Ryuunosuke

22/03/2017 at 21:18
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a) Find x if : |2x + 3| = x + 2

b) Find the smallest value of A = |x - 2006| + |2007 - x| when x change 



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  • ...
    Kurosaki Akatsu Coordinator 22/03/2017 at 21:22

    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = \(\dfrac{-5}{3}\)

    So x = -1 and x = \(\dfrac{-5}{3}\)

    b) We have : 

    A = |x - 2006| + |2007 - x| \(\ge\) |x - 2006 + 2007 - x| = |1| = 1

    \(\Leftrightarrow\left\{{}\begin{matrix}\left|x-2006\right|\le0\\\left|2007-x\right|\le0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2006\\x=2007\end{matrix}\right.\)

    So when x = 2006 ; 2007 then value of A smallest 

    Kayasari Ryuunosuke selected this answer.
  • ...
    Trịnh Đức Phát 22/03/2017 at 21:27

    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = −53

    So x = -1 and x = −53

    b) We have : 

    A = |x - 2006| + |2007 - x| ≥ |x - 2006 + 2007 - x| = |1| = 1

    ⇔{|x−2006|≤0|2007−x|≤0⇒{x=2006x=2007

    So when x = 2006 ; 2007 then value of A smallest 

  • ...
    ๖ۣۜGiang๖ۣۜ 23/03/2017 at 17:41

    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = −53

    So x = -1 and x = −53

    b) We have : 

    A = |x - 2006| + |2007 - x| ≥ |x - 2006 + 2007 - x| = |1| = 1

    ⇔{|x−2006|≤0|2007−x|≤0⇒{x=2006x=2007

    So when x = 2006 ; 2007 then value of A smallest 

  • ...
    Nễu Lả Ánh 24/03/2017 at 17:34
    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = −53

    So x = -1 and x = −53

    b) We have : 

    A = |x - 2006| + |2007 - x| ≥ |x - 2006 + 2007 - x| = |1| = 1

    ⇔{|x−2006|≤0|2007−x|≤0⇒{x=2006x=2007

    So when x = 2006 ; 2007 then value of A smallest 

  • ...
    Nguyễn Đỗ minh Châu 24/03/2017 at 20:11

    Với 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => X = -1

    Với 2x + 3 = - (x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => X =  - 5 3

    X = -1 và x =  - 5 3

    B) Chúng ta có: 

    A = | x - 2006 | + | 2007 - x | ≥  | x - 2006 + 2007 - x | = | 1 | = 1

    ⇔ { | X - 2006 | ≤ 0 | 2007 - x | ≤ 0 ⇒ { x = 2006 x = 2007

    Vì vậy, khi x = 2006; 2007 thì giá trị A nhỏ nhất 

  • ...
    Nễu Lả Ánh 24/03/2017 at 17:34
    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = −53

    So x = -1 and x = −53

    b) We have : 

    A = |x - 2006| + |2007 - x| ≥ |x - 2006 + 2007 - x| = |1| = 1

    ⇔{|x−2006|≤0|2007−x|≤0⇒{x=2006x=2007

    So when x = 2006 ; 2007 then value of A smallest 

  • ...
    Nễu Lả Ánh 24/03/2017 at 17:34
    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = −53

    So x = -1 and x = −53

    b) We have : 

    A = |x - 2006| + |2007 - x| ≥ |x - 2006 + 2007 - x| = |1| = 1

    ⇔{|x−2006|≤0|2007−x|≤0⇒{x=2006x=2007

    So when x = 2006 ; 2007 then value of A smallest 

  • ...
    Lê Nho Khoa 23/03/2017 at 21:00

    a) With 2x + 3 = x + 2

    => 2x - x = 2 - 3

    => x = -1

    With 2x + 3 = -(x + 2)

    => 2x + 3 = -x - 2

    => 2x + x = -2 - 3

    => 3x = -5

    => x = −53

    So x = -1 and x = −53

    b) We have : 

    A = |x - 2006| + |2007 - x| ≥ |x - 2006 + 2007 - x| = |1| = 1

    ⇔{|x−2006|≤0|2007−x|≤0⇒{x=2006x=2007

    So when x = 2006 ; 2007 then value of A smallest 



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