P4 maths

hi!

got a question i'm a bit puzzled on:

find set of values for which |x-1| > 6x-1

i did it in two mins and got 0<x<3.5

i'm not sure whether this is true, because its worth 5 marks!

help!

PK

dont really folow where you gys got that from.

i solved:

x-1 > 6x - 1

and

-x +1 > 6x - 1, and combiined the inequalities... could you explain your method, please.

Phil

Let x >= 1. My graph suggests that |x - 1| <= 6x - 1. To prove this observation, we use the fact that |x - 1| = x - 1. The inequality |x - 1| <= 6x - 1 is equivalent to x - 1 <= 6x - 1, which is equivalent to 5x >= 0, which is true! (Saying that two inequalities are equivalent means that they are either both true or both false.)

So |x - 1| <= 6x - 1 for all x >= 1.

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Hence we need only consider what happens under the assumption that x < 1. Then |x - 1| = 1 - x. The inequality |x - 1| > 6x - 1 is equivalent to 1 - x > 6x - 1, which is equivalent to 2 > 7x, which is equivalent to x < 2/7.

So

|x - 1| <= 6x - 1 for all x with 2/7 <= x < 1
|x - 1| > 6x - 1 for all x < 2/7

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Putting things together,

|x - 1| <= 6x - 1 for all x >= 2/7
|x - 1| > 6x - 1 for all x < 2/7

sorry mate...thanks for your help, but that is well confusing...dno't know where you got all that from...i've been taught another way...think i'll stick to that.

cheers

Phil

sorry mate...thanks for your help, but that is well confusing...dno't know where you got all that from...i've been taught another way...think i'll stick to that.

cheers

Phil

If you don't like the method the other user showed above then why not just solve the equation as an equality and then check in each interval to see which inequality applies?

i now get X>0 and X<(2/7)