9514 1404 393
Answer:
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.
