DS

[cooper2248817]

I had a general question on DS pertaining to the two statements that are always given. My question is are the two statements always correct in their form. For example:

1. 9x<10x

we cant break the above equation as 9<10 or 9>10 because we don't know the sign of X. We have to accept it in its present form.

Am i correct?

[Guest]

9x<10x
0 < 10x-9x
0<x

[StaceyKoprince]

Statements are correct in their given form, but that form can often be manipulated to allow you to deduce some important information. You just can't make any assumptions beyond what they tell you. (eg, they don't tell me whether X is an integer - so I can't just assume it is.)

In this case, if a statement says 9x < 10x, then the only possible values for x are the ones that make this statement true. So ask yourself what numbers, or sets of numbers, would make this true? Zero wouldn't work. 1 would. Anything greater than 1 would. Stuff between zero and 1 would. -1 wouldn't. Negative numbers in general wouldn't. So the only numbers that would make this statement true are positive ones - but those could be integers or decimals / fractions.