Q25 of 32 Page 107

If |x + 2| ≤ 9, then

Given,


|x + 2| ≤ 9


There are two cases,


(x + 2) ≤ 9


⇒ x ≤ 7


⇒ x ∈ (-∞,7] [1]


And


-(x + 2) ≤ 9


⇒ -x – 2 ≤ 9


⇒ -x ≤ 11


⇒ x ≥ -11 [Multiplication by negative inverts the inequality sign]


⇒ x ∈ [-11, ∞) [2]


From [1] and [2], we get


⇒ x ∈ [-11, 7]

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