Final answer:
The correct mathematical statements for three consecutive odd integers summing to 465 are B) x + 1 + x + 3 + x + 5 = 465 and D) 3x + 6 = 465, both representing the same sum with different expressions.
Step-by-step explanation:
The student is asking for the correct mathematical statements that represent the sum of three consecutive odd integers equalling to 465. When we have three consecutive odd integers, we can express them as x, x + 2, and x + 4. The properties of addition, specifically commutativity (A + B = B + A), indicate that the sum remains the same regardless of the order of the addends. In the context of this problem, the sum of the three odd integers would thus be x + (x + 2) + (x + 4), which simplifies to 3x + 6. Therefore, the correct statements representing the situation are:
- B) x + 1 + x + 3 + x + 5 = 465
- D) 3x + 6 = 465
The equations B) and D) correctly describe the sum of three consecutive odd integers equalling to 465, with B) directly stating the sum and D) simplifying the expression.