To solve these inequalities, we need to find the values of x that satisfy the inequality.

1) 2x^2 - 6x + 5 >= 0
To find the values of x that satisfy this inequality, we can first find the roots of the equation 2x^2 - 6x + 5 = 0 by using the quadratic formula:
x = [6 ± sqrt((-6)^2 - 425)]/(2*2) = [6 ± sqrt(36 - 40)] / 4 = [6 ± sqrt(-4)] / 4
Since the roots are imaginary, the inequality 2x^2 - 6x + 5 >= 0 holds for all real values of x.

2) 3x^2 - 9x + 7 <= 0
To find the values of x that satisfy this inequality, we can first find the roots of the equation 3x^2 - 9x + 7 = 0 by using the quadratic formula:
x = [9 ± sqrt((-9)^2 - 437)]/(2*3) = [9 ± sqrt(81 - 84)] / 6 = [9 ± sqrt(-3)] / 6
Since the roots are imaginary, the inequality 3x^2 - 9x + 7 <= 0 holds for all real values of x.

3) 4x^2 - 12x + 9 <= 0
To find the values of x that satisfy this inequality, we can first find the roots of the equation 4x^2 - 12x + 9 = 0 by using the quadratic formula:
x = [12 ± sqrt((-12)^2 - 449)]/(2*4) = [12 ± sqrt(144 - 144)] / 8 = 12 / 8 = 3/2
Since the discriminant is zero, the roots are equal and the inequality 4x^2 - 12x + 9 <= 0 holds when x = 3/2.