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प्रश्न
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
उत्तर
x – 1| ≤ 5
There are two cases,
x – 1 ≤ 5
Adding 1 to L.H.S. and R.H.S
⇒ x ≤ 6
⇒ –(x – 1) ≤ 5
⇒ –x + 1 ≤ 5
Subtracting 1 from L.H.S. and R.H.S.,
⇒ –x ≤ 4
⇒ x ≥ –4
From cases 1 and 2, we have
⇒ –4 ≤ x ≤ 6 ......[i]
Also,
|x| ≥ 2
⇒ x ≥ 2 and
⇒ – x ≥ 2
⇒ x ≤ –2
⇒ x ∈ (`oo`, –2] ∪ [2, `oo`) ......[ii]
Combining equation [i] and [ii], we get
x ∈ [–4, –2] ∪ [2, 6]
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