Question

How do you graph `2(y-1) > 3(x+1)`?

Answer 1

First of all, let's manipulate the expression to isolate the `y` term:

• `2(y-1)=2y-2`
• `3(x+1)=3x+3`.
  So, the expression is equivalent to `2y-2>3x+3`
  Add `2` to both sides:
  `2y>3x+5`
  Divide by `2` both sides:
  `y>3/2 x + 5/2`

Now, it's easy to plot the equation `y=3/2 x+ 5/2`, since it is a line. That line is the graph of the equation, which means the set of points
which realize `y=3/2 x + 5/2`, and you want the set of points composed of all the greater `y`'s. This simply means that you must consider the area above the line to solve the equation, as you can see in the graph:

graph{y>3/2 x + 5/2 [-10, 10, -5, 5]}

Note that the line itself is not part of the solution, because you have the strict inequality and so the set of points `y=3/2 x + 5/2` is not to be considered