Question

Given |x - 2| >= 4, which of the following is true?

Options:
a) x >= 6
b) x <= -2
c) -2 <= x <= 6
d) x <= 2 or x >= 6

Answer 1

The absolute value inequality |x - 2| ≥ 4 can be split into two scenarios, leading to the solutions x ≥ 6 and x ≤ -2. The correct answer is (d) x ≤ 2 or x ≥ 6, which reflects these two solution sets.

Step-by-step explanation:

The question given is 'Given |x - 2| ≥ 4, which of the following is true?' We have to find the range of x that satisfies the absolute value inequality.

The absolute value inequality |x - 2| ≥ 4 means that the distance between x and 2 on the number line is at least 4 units. This gives us two scenarios:

1. x - 2 ≥ 4, which leads to x ≥ 6
2. x - 2 ≤ -4, which leads to x ≤ -2

Therefore, the correct answer is that the value of x is either greater than or equal to 6, or it is less than or equal to -2, which matches option (d) x ≤ 2 or x ≥ 6.