Let's carefully examine the relationship between Charlotte's and Travis's years of service.
1. Understand the problem statement:
- Charlotte has been working for a certain number of years, which we denote by [tex]\( x \)[/tex].
- Travis has been working for precisely 3 years longer than Charlotte.
2. Define the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- Given that Travis has been working 3 years more than Charlotte, we can express his years of service, [tex]\( y \)[/tex], as:
[tex]\[
y = x + 3
\][/tex]
3. Determine the range of [tex]\( y \)[/tex]:
- Since [tex]\( y \)[/tex] is defined as [tex]\( x + 3 \)[/tex], let's consider what this implies about the possible values of [tex]\( y \)[/tex].
- Regardless of the value of [tex]\( x \)[/tex] (as long as [tex]\( x \geq 0 \)[/tex] because the number of years worked cannot be negative), [tex]\( y \)[/tex] will always be greater than or equal to 3 (since [tex]\( y \)[/tex] is always adding 3 to [tex]\( x \)[/tex]).
4. State the conclusion:
- Therefore, the proper condition representing the range of [tex]\( y \)[/tex] can be described by the inequality:
[tex]\[
y \geq 3
\][/tex]
Hence, the correct answer is:
B. [tex]\( y \geq 3 \)[/tex]
