Question

Solve the inequality 13 ≤ -2(y - 4) + 3y and explain your steps.

Answer 1

The inequality is solved by distributing the negative across the parentheses, combining like terms, and isolating y to find that y must be greater than or equal to 5.

Step-by-step explanation:

To solve the inequality 13 ≤ -2(y - 4) + 3y, we can follow these steps:

1. 
   
3. Distribute the -2 across the parentheses: 13 ≤ -2y + 8 + 3y.
4. 
   
6. Combine like terms: 13 ≤ y + 8.
7. 
   
9. Subtract 8 from both sides to isolate y: 5 ≤ y or y ≥ 5.

This means y must be greater than or equal to 5 to satisfy the inequality.