1.

Write the solution set of the inequation |x - 1| ≥ |x - 3|.

Answer»

|x – 1| ≥ |x – 3|

Squaring both sides,

|x – 1|2 ≥ |x – 3|2 

(x – 1)2 ≥ (x – 3)2 

x2 – 2x + 1 ≥ x2 – 6x + 9 

4x – 8 ≥ 0 

x ≥ 2 

x ∈ [2, ∞)



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