Question

Given |x - 2| >= 4, which of the following is true? Question 6

a) x ≤ -6 or x ≥ 6
b) x ≤ -2 or x ≥ 6
c) x ≤ -6 or x ≥ 2
d) x ≤ -2 or x ≥ 2

Answer 1

To solve |x - 2| >= 4, we consider two cases and find that x must be less than or equal to -2 or greater than or equal to 6, matching option (b).

Step-by-step explanation:

To solve the inequality |x - 2| >= 4, we consider two cases because of the absolute value:

1. x - 2 >= 4
2. x - 2 <= -4

For the first case:

1. Add 2 to both sides: x >= 6

For the second case:

1. Add 2 to both sides: x <= -2

Therefore, the set of possible solutions for x is x ≤ -2 or x ≥ 6, which corresponds to option (b).