The correct option is **B. 3(x + 5)**. ### Step-by-Step Explanation: 1. **Understanding the Expression**: The phrase "three times the sum of a number x and five" can be broken down into two parts: - "the sum of a number x and five" - "three times" that sum. 2. **Identifying the Sum**: The sum of a number \( x \) and five can be expressed mathematically as: \[ x + 5 \] This means we are adding the number \( x \) to the number 5. 3. **Applying "Three Times"**: The phrase "three times" indicates that we need to multiply the entire sum \( (x + 5) \) by 3. This can be expressed as: \[ 3 \times (x + 5) \] In mathematical notation, this is often written as: \[ 3(x + 5) \] 4. **Final Expression**: Therefore, the complete expression for "three times the sum of a number \( x \) and five" is: \[ 3(x + 5) \] ### Why Other Options Are Incorrect: - **Option A: 3x + 5** - This expression means "three times \( x \)" plus 5, which does not represent the sum of \( x \) and 5 being multiplied by 3. It is incorrect because it does not follow the order of operations described in the question. - **Option C: 3x + 15** - This expression suggests that we are multiplying \( x \) by 3 and then adding 15. This is also incorrect because it implies that we are adding 15 (which is \( 3 \times 5 \)) to \( 3x \) instead of summing \( x \) and 5 first. - **Option D: 3x - 5** - This expression indicates "three times \( x \)" minus 5. This is incorrect as it does not reflect the sum of \( x \) and 5 at all, and it introduces a subtraction that is not present in the original phrase. ### Common Pitfalls: - **Misinterpreting "three times"**: Students often confuse multiplying just \( x \) by 3 instead of the entire sum. - **Forgetting Parentheses**: Not using parentheses can lead to incorrect interpretations of the order of operations. - **Adding or Subtracting Incorrectly**: Be careful not to add or subtract numbers that are not part of the original expression. ### Revision Summary: - The expression "three times the sum of a number \( x \) and five" translates to \( 3(x + 5) \). - Always identify the components of the expression carefully: what is being summed and what is being multiplied. - Use parentheses to clarify the order of operations in mathematical expressions. - Review each option critically to ensure it matches the original wording of the problem.