Inequality question
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Solve the inequality (2x+1)/(x+1) > or = x+8. Hence solve the inequality (2|x|+1)/(|x|+1) > or = |x|+8
For the first part, I got -1.21 </= x < -1 ( which I think is most likely to be correct even though I do not know the exact answer)
For the second part, I got something like x</=1.21 or x>/=-1.21 (quite weird answers... will someone clarify?)
I merely subsituted |x| into the 'x' in the earlier equation and got-1.21 </= |x| < -1 and this is also equivalent to |x|>/=-1.21 or |x|<-1. After which I did the necessary before arriving at the answer. Did I go wrong somewhere?
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Originally posted by anpanman:
Solve the inequality (2x+1)/(x+1) > or = x+8. Hence solve the inequality (2|x|+1)/(|x|+1) > or = |x|+8
For the first part, I got -1.21 </= x < -1 ( which I think is most likely to be correct even though I do not know the exact answer)
For the second part, I got something like x</=1.21 or x>/=-1.21 (quite weird answers... will someone clarify?)
I merely subsituted |x| into the 'x' in the earlier equation and got-1.21 </= |x| < -1 and this is also equivalent to |x|>/=-1.21 or |x|<-1. After which I did the necessary before arriving at the answer. Did I go wrong somewhere?
For the 1st inequality, bring (2x+1)/(x+1) to the other side, and you will get (x^2+7x+7)/(x+1) less than or equal to zero after simplifying.
x^2+7x+7 = (x+7/2)^2 - 21/4
Thus, the sign changes when at x = sqrt(21/4) -7/2, x = -sqrt(21/4)-7/2 and x= -1.
Draw a number line to figure out when (x^2+7x+7)/(x+1) is less than or equal to zero.
For the 2nd inequality, your positive answers from part 1 will be this part's answers.
(I can give you the solution if you want to.
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Originally posted by Forbiddensinner:
For the 1st inequality, bring (2x+1)/(x+1) to the other side, and you will get (x^2+7x+7)/(x+1) less than or equal to zero after simplifying.
x^2+7x+7 = (x+7/2)^2 - 21/4
Thus, the sign changes when at x = sqrt(21/4) -7/2, x = -sqrt(21/4)-7/2 and x= -1.
Draw a number line to figure out when (x^2+7x+7)/(x+1) is less than or equal to zero.
For the 2nd inequality, your positive answers from part 1 will be this part's answers.
(I can give you the solution if you want to.
)
Dont mind looking at your solution... your steps seem foreign to me compared to what is being taught in my school. hahah. -
Originally posted by anpanman:
Dont mind looking at your solution... your steps seem foreign to me compared to what is being taught in my school. hahah.What have you been taught in school? It'll be easier to advise if you post your working. Basically, Forbiddensinner's steps are correct, whereas your answer for part 1 is missing out on x </= -5.79 so you only have part of the answers.
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Originally posted by anpanman:
Dont mind looking at your solution... your steps seem foreign to me compared to what is being taught in my school. hahah.First of all, did you get (x^2+7x+7)/(x+1) less than or equal to zero?
If you did, use completing the square on (x^2+7x+7) to get ((x+7/2)^2 - 21/4).
You will have ((x+7/2)^2 - 21/4)/(x+1).
Notice that the 3 major points which can possibly result in a change of sign are at sqrt(21/4)-7/2, -sqrt(21/4)-7/2 and -1.
Draw a number line and using these three major points, check for the values of x where ((x+7/2)^2 - 21/4)/(x+1) is less than or equal to zero.
Viola, you are done for the 1st part.
For the 2nd part....wait till you are done with the first then we will talk about it.