Question

victoria is 4 years older than her neighbor. the sum of their ages is no more than 14 years. enter an inequality that can be used to represent this situation in the box, where x represents victorias neighbor’s age.

Explanation:

Step1: Determine Victoria's age

Since Victoria is 4 years older than her neighbor (whose age is \( x \)), Victoria's age is \( x + 4 \).

Step2: Set up the inequality for the sum of their ages

The sum of their ages is Victoria's age plus her neighbor's age, which is \( (x + 4) + x \). This sum is no more than 14, so we write the inequality as \( x + (x + 4) \leq 14 \). Simplifying the left - hand side gives \( 2x+4\leq14 \), but the question just asks for an inequality to represent the situation, and \( x+(x + 4)\leq14 \) (or \( 2x + 4\leq14 \)) is correct. However, we can also write it as \( x+(x + 4)\leq14 \) which simplifies to \( 2x+4\leq14 \), but the most direct form from the sum is \( x+(x + 4)\leq14 \).

Answer:

\( x+(x + 4)\leq14 \) (or equivalently \( 2x + 4\leq14 \))