Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

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

Terms of Service

Privacy Policy

Contact: info@tinkutara.com