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Solve-the-inequality-x-1-x-1-lt-4-

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Question Number 18653 by Tinkutara last updated on 26/Jul/17
Solve the inequality, ∣x − 1∣ + ∣x + 1∣ < 4
Solvetheinequality,∣x−1∣+∣x+1∣<4
Answered by ajfour last updated on 26/Jul/17
If x<−1 −(x−1)−(x+1)<4 ⇒ 2x>−4 or x> −2 hence x∈(−2 ,−1) If −1≤x<1 −(x−1)+x+1<4 ⇒ 2<4 so x∈[−1,1) If 1≤x x−1+x+1<4 ⇒ 2x<4 or x<2 x∈[1,2) Taking union of the three cases, x∈(−2,2) .
Ifx<−1−(x−1)−(x+1)<4⇒2x>−4orx>−2hencex∈(−2,−1)If−1⩽x<1−(x−1)+x+1<4⇒2<4sox∈[−1,1)If1⩽xx−1+x+1<4⇒2x<4orx<2x∈[1,2)Takingunionofthethreecases,x∈(−2,2).
Commented by Tinkutara last updated on 26/Jul/17
Thank you very much ajfour Sir!
ThankyouverymuchajfourSir!
Commented by ajfour last updated on 26/Jul/17

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