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

Apr 3, 2015

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

• $2 \left(y - 1\right) = 2 y - 2$
• $3 \left(x + 1\right) = 3 x + 3$.
So, the expression is equivalent to $2 y - 2 > 3 x + 3$
Add $2$ to both sides:
$2 y > 3 x + 5$
Divide by $2$ both sides:
$y > \frac{3}{2} x + \frac{5}{2}$

Now, it's easy to plot the equation $y = \frac{3}{2} x + \frac{5}{2}$, since it is a line. That line is the graph of the equation, which means the set of points
which realize $y = \frac{3}{2} x + \frac{5}{2}$, 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 $y = \frac{3}{2} x + \frac{5}{2}$ is not to be considered