Final answer:
The solutions to the equation 2|2y-11 + 5 = 19 are y = 9 and y = 2.
Step-by-step explanation:
To solve the equation 2|2y-11 + 5 = 19, we need to isolate the absolute value expression on one side. Subtract 5 from both sides: 2|2y-11 = 14. Divide both sides by 2: |2y-11| = 7. Now we have two cases to consider: 2y-11 = 7 or 2y-11 = -7. Solve each case separately.
Case 1: 2y-11 = 7. Add 11 to both sides: 2y = 18. Divide both sides by 2: y = 9.
Case 2: 2y-11 = -7. Add 11 to both sides: 2y = 4. Divide both sides by 2: y = 2.
Therefore, the solutions to the equation are y = 9 and y = 2.