Which of following is the set of all real numbers x such that `x + 3 > x + 5`?

Options

A. The empty set
B. The set containing all real numbers
C. The set containing all nonnegative real numbers
D. The set containing all positive real numbers

Answer

To solve the inequality \( x + 3 > x + 5 \), we will follow these steps:

### Step 1: Write down the inequality
We start with the given inequality:
\[ x + 3 > x + 5 \]

### Step 2: Subtract \( x \) from both sides
To simplify the inequality, we subtract \( x \) from both sides:
\[ 3 > 5 \]

### Step 3: Analyze the result
The statement \( 3 > 5 \) is false. This means that there are no values of \( x \) that can satisfy the original inequality.

### Conclusion
Since the inequality \( x + 3 > x + 5 \) is never true for any real number \( x \), the solution set is the empty set.

### Final Answer
The set of all real numbers \( x \) such that \( x + 3 > x + 5 \) is the empty set.

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