1/2(4x-2)-2/3(6x+9) is greater than or equal to 4
(1/2)(4x - 2) - (2/3)(6x + 9) >= 4
Multiply both sides by 2 * 3 = 6.
Since you are multiplying by a positive number, then leave the inequality signs as they are.
3(4x - 2) - 4(6x + 9) >= 24
Multiply out the bracketed terms.
12x - 6 - 24x - 36 >= 24
Simplify the terms
-12x - 42 >= 24
-12x - 42 + 42 >= 24 + 42
-12x >= 66
Multiply by -1, so change the direction of the inequality sign
12x <= -66
x <= -66/12 = -11/2
x <= -11/2