Question

The absolute value inequality 1 S-1 will have what type of solution set?

A) Intersection
B) Union
C) All real numbers
D) No solution

Answer 1

The absolute value inequality 1 S-1 will have an intersection type of solution set. The solution set is just x = 1.

Step-by-step explanation:

The absolute value inequality |1 - x| will have an intersection type of solution set.

hen dealing with absolute value inequalities, we consider two cases:

If the expression inside the absolute value is positive, the inequality has the same behavior as an equation without absolute values. So, in this case, we have 1 - x >= 0, which simplifies to x <= 1.

1. If the expression inside the absolute value is negative, we need to negate it to solve the inequality. So, in this case, we have -(1 - x) >= 0, which simplifies to x >= 1.

Therefore, the solution set for the absolute value inequality 1 - x >= 0 is x <= 1 and x >= 1. Since these two sets overlap at x = 1, the solution set is the intersection of these two sets, which is just x = 1.