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Linear Inequalities — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequalities1 Mark
MCQ
Choose the correct answer.
If $|\text{x}+2|\leq9,$ then:
  • A
    $\text{x}\in(-7,11)$
  • B
    $\text{x}\in[-11, 7]$
  • C
    $\text{x}\in[-\infty,-7)\cup(11,\infty) $
  • D
    $\text{x}\in(-\infty,-7)\cup[11,\infty) $
✓

Answer

  1. $\text{x}\in[-11, 7]$

Solution:

Given that $|\text{x}+2|\leq9$

$\Rightarrow-9\leq\text{x}+2\leq9$ 

$\Rightarrow-9-2\leq\text{x}\leq9-2[|\text{x}\leq\text{a}|]$ 

$\Rightarrow-11\leq\text{x}\leq7$

$\Rightarrow\text{x}\in[-11, 7]$

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