Final answer:
The compounded inequality -3(y-2)≤18 or 15+y<18 is solved by treating each part separately. The solution to the inequalities is that y can be any number between -4 and 3, including -4 but not including 3.
Step-by-step explanation:
The question asks to solve the compounded inequality -3(y-2)≤18, or, 15+y<18. We'll start by solving each inequality separately and then combine the results.
For the first inequality -3(y-2)≤18:
- Distribute -3 inside the parentheses: -3*y + 6 ≤ 18.
- Subtract 6 from both sides: -3*y ≤ 12.
- Divide both sides by -3, remembering to reverse the inequality sign: y ≥ -4.
For the second inequality 15+y<18:
- Subtract 15 from both sides: y < 3.
Combining the results from both inequalities:
The overall solution to the compounded inequality is all values of y that satisfy y ≥ -4 and y < 3. So y can be any number between -4 and 3, including -4 but not including 3.