Question

show me how to solve inequalities my professor is one that does all the examples out of the book

Answer 1

One way is simply divide or multiple to get a solution like x>... or x<...
3x>9 --- (divide by 3 to get x...) ---> x>9
5x<4 --- (divide by 5 to get x...) ---> x<0.8

Mind the sign changing when there is a minus sign at the side of the x:
3-x<9
-x<6
x>6 (which is logical. When -x is less than 6, then 6 is more than -x and less than x).

There is another way, which seems to be more difficult, but later on in your life, with more complicated questions, it will be the best solution.
If you have an inequality, you are first going to look where it is equal:
3 - x < 9
will become: 3 -x = 9
then you solve this at the usual way:
-x = 6
x = -6

But you had to solve an inequality, not an equation, so we're going to look whether 3-x is bigger (>) or smaller (<) than 9 in several cases, because we now only know the cases in which it is equal.
Draw a horizontal line on your paper and mark where the two sides of the inequality are equal (x=-6). Draw a little vertical line here (or a dot or heart or whatever you like). Then you go and check both sides: left from x=-6 and right from it. You choose a number left from it (so any number <-6), i.e. -7 and solve the inequality: 3 - (-7) = 10 > 9. So here the left side is bigger than 9. At the other side, you do the same i.e. 0: 3-0 = 3 < 9. Here, the left side is smaller than 9. Now, you can see where the left side is smaller than the right side (that was the question): right from x=-6, so anywhere where x> -6