solve ∣ ∣x−1∣ −2∣ = ∣ x−3 ∣


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 126180 by benjo_mathlover last updated on 18/Dec/20

$s o l v e ∣ ∣ x - 1 ∣ - 2 ∣ = ∣ x - 3 ∣$
	Answered by bobhans last updated on 18/Dec/20

	$(1) f o r x ⩾ 3 \Rightarrow ∣ x - 3 ∣= x - 3$ $(2) f o r x < 3 \Rightarrow∣ 1 - x - 2 ∣= 3 - x$ $∣ - 1 - x ∣ = 3 - x$ $(- 1 - x + 3 - x) (- 1 - x - 3 + x) = 0$ $(2 - 2 x) (- 4) = 0; x = 1$ $s o l u t i o n {1} \cup [3, \infty)$
	Answered by mathmax by abdo last updated on 18/Dec/20
	$∣∣x−1∣−2∣=∣x−3∣ ⇔∣x−1∣−2=x−3(e_1 ) or ∣x−1∣−2=3−x(e_2 ) ∣x−1∣−2=x−3 ⇒∣x−1∣=x−1 ⇒x−1=x−1 or x−1=1−x ⇒ x=1 (e_2 )⇒∣x−1∣−2=3−x ⇒∣x−1∣=5−x (sox≤5) ⇒x−1=5−x or x−1=x−5 ⇒2x=6 or−1=−5(impo) ⇒x=3 so the set of solution is S={1,3}$
	$∣∣ x - 1 ∣ - 2 ∣=∣ x - 3 ∣ \Leftrightarrow∣ x - 1 ∣ - 2 = x - 3 (e_{1}) or ∣ x - 1 ∣ - 2 = 3 - x (e_{2})$ $∣ x - 1 ∣ - 2 = x - 3 \Rightarrow∣ x - 1 ∣= x - 1 \Rightarrow x - 1 = x - 1 or x - 1 = 1 - x \Rightarrow$ $x = 1$ $(e_{2}) \Rightarrow∣ x - 1 ∣ - 2 = 3 - x \Rightarrow∣ x - 1 ∣= 5 - x (sox ⩽ 5) \Rightarrow x - 1 = 5 - x or$ $x - 1 = x - 5 \Rightarrow 2 x = 6 or - 1 = - 5 (impo) \Rightarrow x = 3 so the set of solution$ $is S = {1, 3}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum