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Question Number 155393 by cortano last updated on 30/Sep/21

∣∣x−4∣−4∣ ≥ 4

∣∣x−4∣−4∣⩾4

Answered by mr W last updated on 30/Sep/21

∣x−4∣−4≥4 ⇒∣x−4∣≥8 ⇒x−4≥8 or x−4≤−8 ⇒x≥12 or x≤−4 or ∣x−4∣−4≤−4 ⇒∣x−4∣≤0 ⇒x=4 solution: x≤−4, x=4 or x≥12

∣x−4∣−4⩾4⇒∣x−4∣⩾8⇒x−4⩾8orx−4⩽−8⇒x⩾12orx⩽−4or∣x−4∣−4⩽−4⇒∣x−4∣⩽0⇒x=4solution:x⩽−4,x=4orx⩾12

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