Final answer:
The correct inequality representing the solution to the absolute value inequality 2/2y-31 - 4 < 6 is 2/2y-31 < 10. We solve this by first isolating the absolute value, then considering the conditions when the inside expression is positive and negative.
Step-by-step explanation:
To solve the absolute value inequality 2/2y-31 - 4 < 6, we first isolate the absolute value by adding 4 to both sides of the inequality:
|2/2y-31| < 10
Next, we consider the two scenarios for the absolute value:
If the expression inside is positive, we have 2/2y-31 < 10.
If the expression inside is negative, we have 2/2y-31 > -10.
Since the absolute value expression being greater than -10 isn't restrictive (as the absolute value is always non-negative), this condition is always satisfied and doesn't provide a bound on the solution.
Therefore, the correct inequality that represents the solution to the original inequality is option A: 2/2y-31 < 10.