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∣x−3∣≤5
Which of the following inequalities is equivalent to the absolute value inequality above? 
  • a)
    −2≤ x ≤8
  • b)
    −8≤ x ≤8
  • c)
     
    x≤−2 or x≥8
  • d)
    x≤−8 or x≥2
  • e)
    x≤−3 or x≥9
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
x−3≤5Which of the following inequalities is equivalent to the...
Correct option is A
Rule is when ∣y∣<a
−a<y<a
Now when ∣x−3∣≤5, then 
−7<2x−3≤5
Adding 3 and then dividing on both sides, we get
−5+3≤ x ≤5+3
−2< x <8
Option A.
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