To solve for x, we need to get x by itself on one side of the inequality.
First, we'll start by combining like terms on the left side of the inequality:
2(x - 6) - 3x ≥ -3
2x - 12 - 3x ≥ -3
Combining the two x terms gives us:
-x - 12 ≥ -3
Next, we'll add 12 to both sides to isolate the x term:
-x - 12 + 12 ≥ -3 + 12
-x ≥ 9
Finally, we'll divide both sides by -1 to solve for x:
(-x)/(-1) ≥ 9/(-1)
x ≤ -9
So the solution to the inequality is x ≤ -9.