Question 1138589
<pre>{{{matrix(3,1,

matrix(1,3,3x^2,"">="",10-x),

matrix(1,3,3x^2+x-10,"">="",0),

matrix(1,3,(3x-5)(x+2),"">="",0) )}}}

Find the zeros of the left side, which will be the
critical numbers for the inequality:

{{{matrix(3,1,

matrix(1,5,3x-5=0,"","","",x+2=0),

matrix(1,5,3x=5,"","","",x=-2),

matrix(1,5,x=5/3,"","","",x=-2) )}}}

Draw a number line with the critical numbers marked.
Note that {{{5/3=1&2/3}}}, 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</pre>