Please answer ASP 1. Fill in the blank. When you clear out the fractions in the equation you _.

2. Trey was solving the equation below in class. The teacher has already told Trey his answer is incorrect but he can’t find his mistake. What mistakes has Trey made that are preventing him from getting a correct answer? What is the correct answer?

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  1. multiply both sides by 3

  2. (a) chose to multiply by 2/3 instead of 3/2; (b) did the multiplications incorrectly, both for the fraction and the integer; (c) x = 9

Step-by-step explanation:

1. If you want to "clear fractions," you multiply by the denominator of the fraction.

  3(2/3)x = 3(6)

  2x = 18

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2. The coefficient of x is 2/3. If you want it to be 1, you need to multiply by the multiplicative inverse of 2/3, which is 3/2. Doing that gives ...

  (3/2)(2/3)x = (3/2)6

Then simplifying gives ...

  x = 18/2 = 9

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Trey's mistakes were: a) choosing the wrong multiplier; b) carrying out the multiplication incorrectly. (2/3)(2/3) = 4/9, and 6(2/3) = 4. Had Trey done the multiplications correctly, he would have seen that he needed a different multiplier to get to the answer.

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