Find the zeros of the left side, which will be the
critical numbers for the inequality:
Draw a number line with the critical numbers marked.
Note that 
, so we mark a point about
2/3rds of the way between 1 and 2.
We can go ahead and mark them with darkened circles
since the inequality has 
not 
.
-----------●-----------------●------------
-4 -3 -2 -1 0 1 2 3 4
That identifies three intervals, (-∞,-2], [-2,5/3], [2,∞)
We choose an easy test point, an interior point of each
interval.
interval |test pt. |sign of (3x-5)(x+2) |include in solution?|
(-∞,-2] | x=-3 | + | yes |
[-2,5/3] | x=0 | - | no |
[2,∞) | x=3 | + | yes |
So the number line graph is
<==========●-----------------●===========>
-4 -3 -2 -1 0 1 2 3 4
And so the solution is (-∞,-2] U [5/3,∞)
Edwin
