Final answer:
All possible values of x that satisfy the inequality |x-2|<8 are in the range of -6 < x < 10. This means x can be any number between -6 and 10, exclusive of the end points.
Step-by-step explanation:
The question asks for all possible values of x that satisfy the inequality |x-2| < 8. To solve this, we need to consider both the positive and negative scenarios that come from the absolute value.
Firstly, if x-2 is positive or zero, the absolute value has no effect, and the inequality stays the same:
By adding 2 to both sides, we get:
Secondly, if x-2 is negative, then the absolute value changes the sign:
- -(x - 2) < 8 → -x + 2 < 8
- Adding x to both sides gives us: 2 < 8 + x
- Subtracting 8 from both sides gives us: -6 < x
Combining both scenarios, we have the inequality -6 < x < 10, which is the set of all values that x can take to satisfy the original inequality.