## amorfide 3 years ago 1/x > 1 how to solve?

1. Sir_Rico_of_Eureka

same way as with an equals sign. just leave that alligator mouth there. you need to clear the fractions. try multiplying both sides by the fractions denominator

2. amorfide

okay so i multiply by x on both sides 1>x so why when i have |dw:1350339428053:dw| why when i have this do i multiply by (x-2)² @Sir_Rico_of_Eureka

3. Sir_Rico_of_Eureka

You just multiply both sides again to clear the fractions. this time however you have one more step. get x by itself

4. amorfide

on the question i wrote on the picture, i must multiply by (x-2)² not x-2 i want to know why?

5. amorfide

@cwrw238

6. Sir_Rico_of_Eureka

Who said you have to multiply (x-2)^2. Whats the original problem

7. amorfide

the book because apparently i will lose a solution if i dont

8. Sir_Rico_of_Eureka

Whats the original problem

9. amorfide

|dw:1350339676275:dw|

10. Sir_Rico_of_Eureka

And your book says the solution needs to multiply both sides by (x-2)^2? in the back of the book?

11. amorfide

yes because if i only multiply by x-2 i lose a solution i dont see how

12. amorfide

@TuringTest

13. Sir_Rico_of_Eureka

Hm, If you do the math the same answer comes out. Does it give you an answer to the problem

14. amorfide

|dw:1350340054622:dw|

15. TuringTest

you have to keep in mind that x-2 could be negative, so you need to consider cases

16. Sir_Rico_of_Eureka

I see now, if you look closely simply solving they way we did it at first is saying that x<3 and it can't be a negative number because a negative is never bigger than a positive. Therefore at some number x<3 stops being completly true. How i figured it out is plugged in 2 and saw that it equals 1/0 and you cant divide by zero. Therefore it must be a number between two and three. Thats the logical explanation. But I guess I don't know the specific rules taught in your book.

17. TuringTest

if x-2<0 the sign of the inequality would change upon multiplication, but (x-2)^2 can never be negative, so that we can use without changing the sign of the inequality

18. amorfide

thank you very much people!

19. TuringTest

welcome!