I multiplied the left and right side by 3-x to get rid of it and ended up with 3 is less than or equal to x.

Then I did the same thing but changed the initial equation to x+3/3-x is greater than or equal to 2 and solved.

I didn't get the same answers as the book though.

(x+3)/(3-x) < 2

usually, when solving inequalities, the easiest way to do it is to just set it as an equality, then check your inequalities later... this way, you don't have to worry about flipping the sign when negative, etc. etc.

x+3 = 2(3 - x)

x+3 = 6 - 2x

3x = 3

x = 1

now, make a number line.

and plug in a number that's less than 1 and that's greater than 1 to determine inequality.

Also, don't forget that you have a discontinuity at x = 3