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Linear Inequalities — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLinear Inequalities1 Mark
MCQ
Choose the correct answer. If $|x - 1| > 5,$ then:
  • A
    $\text{x}\in(-4, 6)$
  • B
    $\text{x}\in[-4,6]$
  • ✓
    $\text{x}\in[-\infty,-4)\cup(6,\infty) $
  • D
    $\text{x}\in[-\infty,-4)\cup[6,\infty) $
✓

Answer

Correct option: C.
$\text{x}\in[-\infty,-4)\cup(6,\infty) $
Given that $|x - 1| > 5$
$\Rightarrow (x - 1) < -5$ or $(x - 1) > 5$
$\Rightarrow x < -5 + 1$ or $x > 5 + 1$
$\Rightarrow x < -4$ or $x > 6$
$\Rightarrow\text{x}\in[-\infty,-4)\cup(6,\infty) $

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