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x-1-5-2-has-solution-set-is-a-x-b-or-x-c-x-d-Find-a-d-b-c-

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Question Number 162715 by tounghoungko last updated on 31/Dec/21
∣∣x−1∣−5∣ ≥ 2 has solution set is a ≤x≤b or x≤ c ∪ x≥d . Find ((a+d)/(b+c)) .
∣∣x−1∣−5∣⩾2hassolutionsetisa⩽x⩽borx⩽c∪x⩾d.Finda+db+c.
Answered by bobhans last updated on 01/Jan/22
∣∣x−1∣−5∣ ≥2 ⇒ (∣x−1∣−7)(∣x−1∣−3)≥0 ⇒ ∣x−1∣ ≤3 ∪ ∣x−1∣ ≥7 ⇒ −2≤x≤4 ∪ x≤−6 ∪ x≥ 8 { ((a=−2 ∧ b=4 )),((c=−6 ∧ d=8)) :} ⇒((a+d)/(b+c)) = (6/(−2))= −3
∣∣x−1∣−5∣⩾2⇒(∣x−1∣−7)(∣x−1∣−3)⩾0⇒∣x−1∣⩽3∪∣x−1∣⩾7⇒−2⩽x⩽4∪x⩽−6∪x⩾8{a=−2∧b=4c=−6∧d=8⇒a+db+c=6−2=−3
Answered by MJS_new last updated on 31/Dec/21
∣∣x−1∣−5∣≥2 (1) x≥1 ⇒ ∣x−6∣≥2 (1.1) x≥6 ⇒ x−6≥2 ⇒ x≥8 (1.2) 1≤x<6 ⇒ 6−x≥2 ⇒ 1≤x≤4 (2) x<1 ⇒ ∣x+4∣≥2 (2.1) −4<x<1 ⇒ x+4≥2 ⇒ −2≤x<1 (2.2) x≤−4 ⇒ −x−4≥2 ⇒ x≤−6 ===== x≤−6∨−2≤x≤4∨8≤x a=−2, b=4, c=−6, d=8 ⇒ ((a+d)/(b+c))=−3
∣∣x−1∣−5∣⩾2(1)x⩾1⇒∣x−6∣⩾2(1.1)x⩾6⇒x−6⩾2⇒x⩾8(1.2)1⩽x<6⇒6−x⩾2⇒1⩽x⩽4(2)x<1⇒∣x+4∣⩾2(2.1)−4<x<1⇒x+4⩾2⇒−2⩽x<1(2.2)x⩽−4⇒−x−4⩾2⇒x⩽−6=====x⩽−6∨−2⩽x⩽4∨8⩽xa=−2,b=4,c=−6,d=8⇒a+db+c=−3

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