In order to find the solution set for the given inequality, we just have to isolate the variable x on one side of the expression, like this:
-4x + 10 ≥ 5x + 55
add 4x on both sides
-4x + 4x + 10 ≥ 5x + 4x + 55
0 + 10 ≥ 9x + 55
10 ≥ 9x + 55
Subtract 55 on both sides
10 - 55 ≥ 9x + 55 - 55
-45 ≥ 9x + 0
-45 ≥ 9x
On both sides, divide by 9
-45/9 ≥ 9x/9
-5 ≥ x
Then, the solution set for this inequality is all the numbers that are less or equal to -5, that is:
x ≤ -5