Final answer:
The inequality to represent Victoria being 4 years older than her neighbor with their combined ages not exceeding 14 years is x + (x + 4) ≤ 14, which simplifies to x ≤ 5 after solving.
Step-by-step explanation:
The inequality to represent the situation where Victoria is 4 years older than her neighbor and the sum of their ages is no more than 14 can be represented as x + (x + 4) ≤ 14. This means that if we let x represent the age of the neighbor, then Victoria's age would be x + 4. The sum of their ages should be less than or equal to 14. To find the inequality that describes this situation, we add the two expressions together: x (the neighbor's age) plus x + 4 (Victoria's age), which must be less than or equal to 14.
To solve for x, we combine like terms: 2x + 4 ≤ 14. Subtracting 4 from both sides of the inequality gives us 2x ≤ 10. Finally, dividing both sides by 2, we find that x ≤ 5. This means the neighbor's age can be at most 5 years old, and Victoria's age can be at most 9 years old.