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0 votes
2.3k views
in Linear Equations by (15.2k points)

Find the solution set of the in equation |x – 1| < 2.

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1 Answer

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by (15.7k points)

|x – 1| < 2 

Square both sides 

⇒ (x – 1)2 < 4 

⇒ x 2 – 2x + 1 < 4 

⇒ x 2 – 2x – 3 < 0

⇒ x 2 – 3x + x – 3 < 0 

⇒ x(x – 3) + 1(x – 3) < 0 

⇒ (x + 1)(x – 3) < 0 

Observe that when x > 3 (x – 3)(x + 1) is positive 

And for each root the sign changes hence

We want less than 0 that is negative part 

Hence x should be between -1 and 3 for (x – 3)(x + 1) to be negative 

Hence x ∈ (-1, 3) 

Hence solution set for |x – 1| < 2 is (-1, 3)

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