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30 Jan 2025, 09:59
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:27) correct
0% (00:00) wrong based on 3 sessions
History
Date
Time
Result
Not Attempted Yet
If \(3x = 2(5 – 2x), \) then \( x =\)
A. \(\frac{-10}{7}\)
B. 0
C. \(\frac{3}{7}\)
D. 1
E. \(\frac{10}{7}\)
A. \(\frac{-10}{7}\)
B. 0
C. \(\frac{3}{7}\)
D. 1
E. \(\frac{10}{7}\)
01 Feb 2025, 08:12
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OE
Since plugging in 0 is so much easier than plugging in 3/7, start with B: then the left-hand side of the equation is 0 and the right-hand side is 10. The lefthand side is much too small. Eliminate A and B and try something bigger—D, of course; it will be much easier to deal with 1 than with 3/7 or 10/7. Now the left hand side is 3 and the right-hand side is 6. We’re closer, but not there. The answer must be E. Notice that we got the right answer without ever plugging in one of those unpleasant fractions. Are you uncomfortable choosing E without checking it? Don’t be. If you know that the answer is greater than 1, and only one choice is greater than 1, that choice has to be right.
Again, we emphasize that, no matter what the choices are, you backsolve only if you can’t easily do the algebra. Most students would probably do this problem directly:
\(3x=2(5-2x) = 3x=10-4x=7x=10 = x= \frac{10}{7}\)
and save backsolving for a harder problem. You have to determine which method is best for you.
Since plugging in 0 is so much easier than plugging in 3/7, start with B: then the left-hand side of the equation is 0 and the right-hand side is 10. The lefthand side is much too small. Eliminate A and B and try something bigger—D, of course; it will be much easier to deal with 1 than with 3/7 or 10/7. Now the left hand side is 3 and the right-hand side is 6. We’re closer, but not there. The answer must be E. Notice that we got the right answer without ever plugging in one of those unpleasant fractions. Are you uncomfortable choosing E without checking it? Don’t be. If you know that the answer is greater than 1, and only one choice is greater than 1, that choice has to be right.
Again, we emphasize that, no matter what the choices are, you backsolve only if you can’t easily do the algebra. Most students would probably do this problem directly:
\(3x=2(5-2x) = 3x=10-4x=7x=10 = x= \frac{10}{7}\)
and save backsolving for a harder problem. You have to determine which method is best for you.
