Here's the question you clicked on:
amorfide
1/x > 1 how to solve?
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
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
You just multiply both sides again to clear the fractions. this time however you have one more step. get x by itself
on the question i wrote on the picture, i must multiply by (x-2)² not x-2 i want to know why?
Who said you have to multiply (x-2)^2. Whats the original problem
the book because apparently i will lose a solution if i dont
Whats the original problem
And your book says the solution needs to multiply both sides by (x-2)^2? in the back of the book?
yes because if i only multiply by x-2 i lose a solution i dont see how
Hm, If you do the math the same answer comes out. Does it give you an answer to the problem
you have to keep in mind that x-2 could be negative, so you need to consider cases
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.
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
thank you very much people!