Question

Which of the following inequalities represents the solution to the absolute value inequality 2/2y-31 - 4 < 6?

A. 2/2y-31 < 10
B. 2/2y-31 > 10
C. 2/2y-31 > -2
D. 2/2y-31 < -2

Answer 1

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.