Given that $$ x \leq 12 \frac{1}{4} $$, write down the largest possible value of $$ x $$ if: 1.3.1 $$ x $$ is an integer 1.3.2 $$ x $$ is a prime number 1.3.3 $$ x $$ is a rational number

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UpStudy AI · Accepted Answer

To solve the problem, we need to analyze the condition $$ x \leq 12 \frac{1}{4} $$.

First, let's convert $$ 12 \frac{1}{4} $$ into an improper fraction:
$$
12 \frac{1}{4} = 12 + \frac{1}{4} = \frac{48}{4} + \frac{1}{4} = \frac{49}{4}
$$
This means $$ x $$ must be less than or equal to $$ \frac{49}{4} $$ or $$ 12.25 $$.

Now, let's address each part of the problem:

### 1.3.1 $$ x $$ is an integer
The largest integer less than or equal to $$ 12.25 $$ is $$ 12 $$.

### 1.3.2 $$ x $$ is a prime number
The prime numbers less than or equal to $$ 12.25 $$ are $$ 2, 3, 5, 7, 11 $$. The largest prime number in this list is $$ 11 $$.

### 1.3.3 $$ x $$ is a rational number
Rational numbers include all integers, fractions, and terminating or repeating decimals. The largest rational number less than or equal to $$ 12.25 $$ can be expressed as $$ 12.25 $$ itself, since it is a rational number.

### Summary of Results
1. The largest integer $$ x $$ is $$ 12 $$.
2. The largest prime number $$ x $$ is $$ 11 $$.
3. The largest rational number $$ x $$ is $$ 12.25 $$.
- Largest integer $$ x $$: 12 - Largest prime number $$ x $$: 11 - Largest rational number $$ x $$: 12.25

Given that \( x \leq 12 \frac{1}{4} \), write down the largest possible value of \( x \) if: 1.3.1 \( x \) is an integer 1.3.2 \( x \) is a prime number 1.3.3 \( x \) is a rational number

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