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Linear Inequations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLinear Inequations1 Mark
MCQ
If $\text{|x}+2|\leq9,$ then :
  • A
    $\text{x}\in(-7,11)$
  • B
    $\text{x}\in[-11,7]$
  • ✓
    $\text{x}\in(-\infty,-7)\cup(11,\infty)$
  • D
    $\text{x}\in(-\infty,-7)\cup[11,\infty)$
✓

Answer

Correct option: C.
$\text{x}\in(-\infty,-7)\cup(11,\infty)$
$|\text{x}+2|\leq9$
$\Rightarrow-9\leq\text{x}+2\leq9$
$\Rightarrow-9-2\leq\text{x}+2-2\leq9-2$
$\Rightarrow-11\leq\text{x}\leq7$
$\Rightarrow\text{x}\in[-11,7]$
$\text{x}\in(-\infty,-7)\cup(11,\infty)$

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