Final answer:
The solution set for the inequality 12-4w > 2(w-18) is w < 8.
Step-by-step explanation:
To find the solution set for the inequality 12-4w > 2(w-18), we first simplify the expression on both sides of the inequality.
Starting with the left side, we combine like terms:
12 - 4w = 12 - 4w.
Next, we distribute the 2 on the right side:
2(w-18) = 2w - 36.
Now we have 12 - 4w > 2w - 36.
To isolate the variable w, we can subtract 2w from both sides:
12 - 4w - 2w > -36.
Simplifying further, we get -6w > -48.
Dividing both sides by -6, we have w < 8.
Therefore, the solution set for 12-4w > 2(w-18) is w < 8.