Final answer:
The inequality -32 < 4y - 8 ≤ 28 is solved by adding 8 to all parts and then dividing by 4, resulting in -6 < y ≤ 9. The solution in interval notation is (-6, 9].
Step-by-step explanation:
The student has presented an inequality that needs to be solved for the variable y. To solve the inequality -32 < 4y - 8 ≤ 28, we need to perform two steps.
First, add 8 to all sides of the inequality to isolate the term with the variable on one side. This gives us -24 < 4y ≤ 36. The next step is to divide all sides by 4 to solve for y. The result is -6 < y ≤ 9. The solution in interval notation, expressed in decimal form, is (-6, 9].