Absolute Value Inequality Challenge
∣ ∣ ∣ ∣ 1 − 1 + ∣ x ∣ ∣ x ∣ ∣ ∣ ∣ ∣ ≥ 2 1
The solution set to this inequality is a ≤ x ≤ b . What is b − a ?
The answer is 2.
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1 solution
∣ 1 + ∣ x ∣ 1 + ∣ x ∣ − 1 ∣ ≥ 2 1 The inequality becomes ∣ 1 + ∣ x ∣ 1 ∣ ≥ 2 1 ⇒ 1 + ∣ x ∣ 1 ≥ 2 1 ⇒ 1 + ∣ x ∣ ≤ 2 ⇒ ∣ x ∣ ≤ 1 ⇒ − 1 ≤ x ≤ 1 Hence answer is 1 − ( − 1 ) = 2
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can u tell why in 3rd step only 1 part of the inequality was checked???
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because the other part is a nonsensical inequality, |x|< -3 a absolute value will never be less than -3
@Sanjeet Raria thank you , how it can happen that besides you and @Rishi Hazra the other five , did"nt reported.
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it has happened with me many times. sometimes i post problems with wrong statement by mistake & many people solve tha instead.
I did it the exact same way!!
in the 3rd step where is the other modulus?(the one that was on whole term)
absolute value and positive values make the fraction positive. thus the 2nd module does not exist.
See solution below.