Solve-x-1-x-2-4-

Question Number 170868 by Tawa11 last updated on 01/Jun/22

Solve : ∣ x - 1 ∣ + ∣ x - 2 ∣ ⩾ 4

Answered by thfchristopher last updated on 02/Jun/22

\Rightarrow∣ x - 1 ∣⩾ 4 - ∣ x - 2 ∣

\Rightarrow x - 1 ⩾ 4 - ∣ x - 2 ∣ or x - 1 ⩽∣ x - 2 ∣ - 4

Case 1 :

x - 1 ⩾ 4 - ∣ x - 2 ∣

\Rightarrow∣ x - 2 ∣⩾ 5 - x

\Rightarrow x - 2 ⩾ 5 - x or x - 2 ⩽ x - 5 (rejected)

\Rightarrow 2 x ⩾ 7

\Rightarrow x ⩾ \frac{7}{2}

Case 2 :

x - 1 ⩽∣ x - 2 ∣ - 4

\Rightarrow∣ x - 2 ∣⩾ x + 3

\Rightarrow x - 2 ⩾ x + 3 (rejected) or x - 2 ⩽ - x - 3

\Rightarrow 2 x ⩽ - 1

\Rightarrow x ⩽ - \frac{1}{2}

Conclusion : x ⩽ - \frac{1}{2} or x ⩾ \frac{7}{2}

Commented by Tawa11 last updated on 02/Jun/22

God bless you sir .

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