Final answer:
To solve the inequality |y - 8| + 11 ≥ 19, we subtract 11 from both sides, split into two cases considering the absolute value, and solve for y to obtain y ≤ 0 or y ≥ 16 as the solution.
Step-by-step explanation:
The task is to solve the inequality |y – 8| + 11 ≥ 19. To tackle this, we begin by isolating the absolute value on one side of the inequality.
Step 1: Subtract 11 from both sides of the inequality: |y - 8| ≥ 19 - 11.
Step 2: Simplify the right side: |y - 8| ≥ 8.
Step 3: Recognizing that an absolute value inequality represents two separate inequalities, split the inequality into its two cases.
- Case 1 (positive case): y - 8 ≥ 8
- Case 2 (negative case): y - 8 ≤ -8
Step 4: Solve each case separately,
- For Case 1: y ≥ 8 + 8, which simplifies to y ≥ 16.
- For Case 2: y ≤ -8 + 8, which simplifies to y ≤ 0.
Step 5: Combine the solutions for both cases to get the final solution of the inequality as y ≤ 0 or y ≥ 16.
Remember to check the solutions in the original inequality to ensure accuracy.