Aug 28, 2007 #1 T tomcenjerrym Newbie level 4 Joined Aug 28, 2007 Messages 5 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,281 Activity points 1,330 Does anyone can solve the following equation? |x − 1| = 1 − x Thanks Tom
Aug 28, 2007 #2 A A.Anand Srinivasan Advanced Member level 5 Joined Oct 15, 2005 Messages 1,792 Helped 257 Reputation 514 Reaction score 39 Trophy points 1,328 Location India Activity points 10,678 Re: Inequality question x=1 is the solution.... when x-1 is assumed to be negative we cannot obtain the solution....
Re: Inequality question x=1 is the solution.... when x-1 is assumed to be negative we cannot obtain the solution....
Aug 28, 2007 #3 A Andrew8611 Member level 1 Joined Mar 16, 2006 Messages 37 Helped 1 Reputation 2 Reaction score 1 Trophy points 1,288 Activity points 1,557 Re: Inequality question just do a variable change y=x-1 and -y=1-x, so we will get Abolute value of y=-y so the only number that fits this equation is y=0 so if x-1=0 the solution is x=1.
Re: Inequality question just do a variable change y=x-1 and -y=1-x, so we will get Abolute value of y=-y so the only number that fits this equation is y=0 so if x-1=0 the solution is x=1.
Aug 29, 2007 #4 G Ghitani Junior Member level 3 Joined Jul 3, 2007 Messages 29 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,281 Activity points 1,432 Re: Inequality question The solution is : x= ] - ∞ 1] This because any value of x less than or equlal to 1 would satisfy the equation
Re: Inequality question The solution is : x= ] - ∞ 1] This because any value of x less than or equlal to 1 would satisfy the equation
Sep 5, 2007 #5 D Dmitrij Advanced Member level 4 Joined Jul 14, 2007 Messages 101 Helped 18 Reputation 36 Reaction score 6 Trophy points 1,298 Activity points 2,302 Re: Inequality question All of you must remind a well-known definition of the absolute number's value. It states the following: |a| = a, if a>=0 = -a, otherwise Therefore, your example |x − 1| = 1 − x results in the inequality: x - 1 <= 0 x <=1 It's one of these unique rare cases when inequality is the satisfactory solution of the equation (usually, it's a number or some ones) With respect, Dmitij
Re: Inequality question All of you must remind a well-known definition of the absolute number's value. It states the following: |a| = a, if a>=0 = -a, otherwise Therefore, your example |x − 1| = 1 − x results in the inequality: x - 1 <= 0 x <=1 It's one of these unique rare cases when inequality is the satisfactory solution of the equation (usually, it's a number or some ones) With respect, Dmitij
Sep 15, 2007 #6 H hakeen Full Member level 5 Joined Jun 16, 2005 Messages 240 Helped 44 Reputation 88 Reaction score 19 Trophy points 1,298 Activity points 2,783 Re: Inequality question x<=-1
Sep 16, 2007 #7 S scintillatingstuffs Junior Member level 3 Joined Jun 4, 2006 Messages 27 Helped 5 Reputation 10 Reaction score 1 Trophy points 1,283 Activity points 1,430 Re: Inequality question Use |x|=x if x>0 and |x|=-x if x<0 thus the eqn presents no soluton for |x-1|>0.... But all values are satisfying the soln. for |x-1|<0 Thus x<=1 is the answer.....
Re: Inequality question Use |x|=x if x>0 and |x|=-x if x<0 thus the eqn presents no soluton for |x-1|>0.... But all values are satisfying the soln. for |x-1|<0 Thus x<=1 is the answer.....
Nov 3, 2007 #8 A aersoy Member level 3 Joined Aug 8, 2006 Messages 60 Helped 2 Reputation 4 Reaction score 1 Trophy points 8 Location ankara turkey Activity points 0 Re: Inequality question | x - 1 | = 1 - x = - ( x -1 ) this means that x -1 < 0 (((( not x - 1 <= 0 )))) >>> some of the replies are wrong >> x - 1 < 0 >>> x < 1 solution : (-∞ , 1 ]
Re: Inequality question | x - 1 | = 1 - x = - ( x -1 ) this means that x -1 < 0 (((( not x - 1 <= 0 )))) >>> some of the replies are wrong >> x - 1 < 0 >>> x < 1 solution : (-∞ , 1 ]