Question:
the solution of the inequality l x-1l <2 is
Answer:
Given, |x – 1| < 2
Square both sides, we get
⇒ (x – 1)2 < 4
⇒ x2 – 2x + 1 < 4
⇒ x2 – 2x – 3 < 0
⇒ x2 – 3x + x – 3 < 0
⇒ x(x – 3) + 1(x – 3) < 0
⇒ (x + 1)(x – 3) < 0
Now, draw the figure for it.
From the figure, we observe that when x > 3, (x – 3)(x + 1) is positive and for each root the sign
changes. Now, we want less than 0 that is negative part.
So, x should be between -1 and 3 for (x – 3)(x + 1) to be negative.
Therefore, x ∈ (-1, 3)
Hence, the solution set for |x – 1| < 2 is (-1, 3)
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