Given:
1 - (- 6k + 6) ≤ 3k + 1 + 5k
Let's solve the inequality for k.
USe distributive property to expand the parenthesis:
1 + 6k - 6 ≤ 3k + 1 + 5k
Add 6 to both sides:
1 + 6k - 6 + 6 ≤ 3k + 1 + 5k + 6
1 + 6k ≤3k + 5k + 6 + 1
1 + 6k ≤ 3k + 5k + 7
1 + 6k ≤ 8k + 7
Subtract 8k from both sides:
1 + 6k - 8k ≤ 8k - 8k + 7
1 - 2k ≤ 7
Subtract 1 from both sides:
1 - 1 - 2k ≤ 7 - 1
-2k ≤ 6
Divide both sides by -2:

The inequality sign was flipped because we divided both sides by a negative value. (The inequality sign should only be flipped when you multiply or divide both sides with a negative number)
ANSWER:
k ≥ -3