To solve the inequality 7y - (4y + 2) > -41, we can follow these steps:
1. Distribute the negative sign to the terms inside the parentheses:
7y - 4y - 2 > -41
2. Combine like terms on the left side of the inequality:
3y - 2 > -41
3. Add 2 to both sides of the inequality to isolate the variable:
3y - 2 + 2 > -41 + 2
3y > -39
4. Divide both sides of the inequality by 3 to solve for y:
(3y)/3 > (-39)/3
y > -13
Therefore, the solution to the inequality 7y - (4y + 2) > -41, in set builder notation, is: y > -13.