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  • If |x – 1| > 5, then A.x ∈ (–4, 6) B. x ∈ [–4, 6] C. x ∈ [–∞, –4) ∪ (6, ∞) D. x ∈ [–∞, –4) ∪ [6, ∞)

If \left | x-1 \right |> 5 then

A. x\epsilon \left ( -4,6 \right )

B. x\epsilon \left [ -4,6 \right ]

C.x\epsilon \left [ -\infty ,-4 \right )\upsilon \left ( 6,\infty \right )

D. x\epsilon \left [ -\infty ,-4 \right )\upsilon \left [ 6,\infty \right )

Answers (1)

Given:    |x-1|> 5

Thus, there will be two cases,

(x-1) > 5, x > 6 → x \epsilon (6,∞)     …….. (i)

& -(x-1) > 5 → -x + 1 > 5 → -x > 4

i.e., x < -4

x \epsilon (-∞, -4)  …… (ii)

Therefore, x \epsilon  (-∞, -4) U  (6,∞)

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