Question

solve: |y - 9| + 8 = 13. use a comma to separate solutions, as needed. enter each solution as an integer or reduced fraction. decimal answers will not be accepted. if there is no solution, type dne in the answer box. y = question help: video written example message instructor submit question

Explanation:

Step1: Isolate the absolute value

Subtract 8 from both sides.
$$|y - 9| + 8 - 8 = 13 - 8$$
$$|y - 9| = 5$$

Step2: Split into two linear equations

Absolute value equals 5 means two cases:
Case 1: $y - 9 = 5$
Case 2: $y - 9 = -5$

Step3: Solve Case 1

Add 9 to both sides.
$$y = 5 + 9$$
$$y = 14$$

Step4: Solve Case 2

Add 9 to both sides.
$$y = -5 + 9$$
$$y = 4$$

Answer:

4, 14