Question

Question 10 of 46 What are all possible values of x for which |x-2|<8?

Answer 1

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:

• x - 2 < 8

By adding 2 to both sides, we get:

• x < 10

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.