Which expression represents all the values of $x$, when $x$ is the age ranging from 18 to 24 years old?
A. $(x<18)$ and $(x>24)$
B. $(x>=18)$ and $(x<=24)$
C. $(x<18)$ or $(x>24)$
D. $(x>=18)$ or $(x<=24)$
Answer (2)
The age x must be greater than or equal to 18: x ≥ 18 .
The age x must be less than or equal to 24: x ≤ 24 .
Combine these conditions using 'and': ( x ≥ 18 ) and ( x ≤ 24 ) .
The correct expression is: ( x ≥ 18 ) and ( x ≤ 24 ) .
Explanation
Understanding the Problem We are given that x represents the age ranging from 18 to 24 years old, inclusive. This means x can be any value from 18 up to and including 24. We need to find the expression that correctly represents this range.
Expressing the Lower Bound The age x must be greater than or equal to 18. This can be written as x ≥ 18 .
Expressing the Upper Bound The age x must be less than or equal to 24. This can be written as x ≤ 24 .
Combining the Conditions Since both conditions must be true simultaneously, we combine them using 'and'. So, the correct expression is ( x ≥ 18 ) and ( x ≤ 24 ) .
Identifying the Correct Option Comparing this with the given options, we find that the correct expression is ( x ≥ 18 ) and ( x ≤ 24 ) .
Examples
Understanding age ranges is crucial in many real-life scenarios. For example, certain activities or purchases might be restricted based on age. If a store has a policy that only people aged 18 to 24 can purchase a specific product, the expression ( x ≥ 18 ) and ( x ≤ 24 ) accurately defines the eligible age group. This concept extends to voting eligibility, driving licenses, and even participating in research studies where age-specific data is required. Knowing how to represent such ranges mathematically helps in clearly defining and understanding these criteria.
The expression representing the age of x ranging from 18 to 24 years old is ( x ≥ 18 ) and ( x ≤ 24 ) . Thus, the correct choice is option B. This means x can be any value from 18 to 24, inclusive.
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