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x^2 - 5x + 6  =< 0

First let us factor:

(x-3)(x-2) =< 0

Then we have two cases:

case 1:

x-3 =< 0    and     x-2  => 0

x =< 3    and   x => 2

==> x = [ 2, 3]

 

case 2:

x-3 => 0     and x-2 =< 0

==> x => 3     and   x =< 2    (impossible)

then the solution is:

x = [2, 3]

 

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