2. 外语
  3. DOne way to approach this question is to plug in numbers for the variables and see what the relationship between the two quantit

DOne way to approach this question is to plug in numbers for the variables and see what the relationship between the two quantit

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答案D
解析 One way to approach this question is to plug in numbers for the variables and see what the relationship between the two quantities is for each of the numbers you plug in.
    If you plug in x = 2, you see that Quantity A is 3x+1= 33 or 27, and Quantity B is 4x = 42, or 16. In this case, Quantity A is greater than Quantity B.
    If you plug in x = 3, you see that Quantity A is 3x+1 = 34, or 81, and Quantity B is 4x= 43, or 64. In this case, Quantity A is greater than Quantity B.
    If you plug in x = 4, you see that Quantity A is 3x+1 = 35 or 243, and Quantity B is 4x = 44, or 256. In this case, Quantity B is greater than Quantity A. Since for x = 2 and for x= 3, Quantity A is greater than Quantity B, and for x= 4, Quantity B is greater than Quantity A, it follows that the relationship between the two quantities cannot be determined. The correct answer is Choice D.
    Since both quantities are algebraic expressions, another way to approach this problem is to set up a placeholder relationship between the two quantities and simplify it to see what conclusions you can draw.

For any value of x, the value of 3x is positive, so dividing by 3x does not change any inequality that could be put in the placeholder. Since each step in this simplification is reversible, this reduces the problem to comparing 3 with ;(4/3)x.
    You can see that because 4/3 is greater than 1, the value of(4/3)x becomes greater as x becomes larger. In particular, it is greater than 3 for large enough values of x.
For the smallest value of x, x = 2, the relationship is(4/3)2= 16/9< 3.
    Since for x = 2, Quantity A is greater than Quantity B and for large values of x, Quantity B is greater than Quantity A, it follows that the relationship between the two quantities cannot be determined. The correct answer is Choice D.
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