Question

|3x - 2y| > 8

What are the two inequalities?
a) 3x - 2y > 8 and 3x - 2y < -8
b) 3x - 2y > -8 and 3x - 2y < 8
c) 3x - 2y > 8 and 3x - 2y > -8
d) 3x - 2y < -8 and 3x - 2y < 8

Answer 1

The two inequalities derived from the absolute value inequality |3x - 2y| > 8 are 3x - 2y > 8 and 3x - 2y < -8, which correspond to the positive and negative cases inside the absolute value.

Step-by-step explanation:

The student has asked about solving the inequality |3x - 2y| > 8. To find the two inequalities represented by this absolute value inequality, we need to consider both the positive and the negative scenarios of the expression inside the absolute value. We remove the absolute value by setting up two separate inequalities:

1. If 3x - 2y is positive, then 3x - 2y > 8.
2. If 3x - 2y is negative, then -(3x - 2y) > 8, which simplifies to 3x - 2y < -8.

Therefore, the correct answer to the student's question is: a) 3x - 2y > 8 and 3x - 2y < -8. This is because the absolute value inequality must be greater than 8 for both the positive and negative cases of the expression inside.