Question 40422
{{{-2*x^2+7*x-10 <= (-3)*x+2}}} given
{{{-2*x^2+10*x-10 <= 2}}}       subtracted (-3)*x from both sides
{{{-x^2+5*x-5 <= 1}}}           multiplied both sides by 1/2
{{{-x^2+5*x-6 <= 0}}}           subtracted 1 from both sides
{{{x^2-5*x+6 >= 0}}}            multiplied both sided by -1

Factoring left side yields
(x-3)(x-2) >= 0

The values of x for which x-2=0 or x-3=0 are x=2 and x=5. These points divide the coordinate line into three intervals,
    (-inf,2], (2,3) and [3, +inf)

We need to check points of which of these three intervals give positive sign for the product (x-3(x-2). We shall choose arbitrary points on each of these intervals to determine the sign; these points are called test points. Lets say 1, 2.5 and 4 will be the test points for intervals (-inf,2], (2,3) and [3, +inf) respectively.

For interval (-inf,2] with test point 1 sign of (x-2)(x-3) is (-)(-) = +
For interval (2,3) with test point 2.5  sign of (x-2(x-3)  is (+)(-) = -
For interval [3,+inf)with test point 4 sign of (x-2(x-3) is  (+)(+) = +

The pattern of signs suggest that the solution set is 
(-inf,2] U [3,+inf)