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“It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.” — Carl F. Gauss

Carl Friedrich Gauss — German mathematician, astronomer & physicist · 1777–1855. Widely regarded as one of the greatest mathematicians in history, his remarkable talent for numbers started when he was a young child.

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Algebra · Set 34 of 12

Solve for x

3x + 7 = 22

x = 4

x = 5

x = 6

x = 7

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Formatted

x =−b ± √(b² − 4ac)2a

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Accuracy

78%

36 pts

42%
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W8

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Problem 21

Reviewed

Solve for m

\frac{5 [2 - (\frac{3 m + 1}{4} - \frac{m - 2}{5})]}{13} - \frac{3 [\frac{2 m + 3}{6} - (1 - \frac{m}{4})]}{11} = \frac{43}{52}

5 attempts

Wrong to right

$\frac{(2 - (\frac{3 m + 1}{4} - \frac{m - 2}{5}))}{13} - \frac{3 (\frac{2 m + 3}{6} - (1 - \frac{m}{4}))}{11} = \frac{43}{52}$
Your work has a critical error right at the start. The first term in the problem is 5 times [the bracket] divided by 13, but you wrote it without the 5. This changes all the calculations that follow. Go back and keep that 5 multiplier, it matters a lot for the final answer.
$\frac{5 [2 - (\frac{3 m + 1}{4} - \frac{m - 2}{5})]}{13} - \frac{3 (\frac{2 m + 3}{6} - (1 - \frac{m}{12}))}{11} = - \frac{43}{52}$
Your final answer m = 4 is correct, well done! However, your working has some unclear jumps and possible copying mistakes in the middle steps, which made it hard to follow. Try to show each simplification step more carefully and check your fractions as you go.
$5 [\frac{3 m + 1}{4} - \frac{m - 2}{5}] - \frac{3 (\frac{2 m + 3}{6} - (1 + \frac{m}{10}))}{11} = - \frac{43}{52}$
Your final answer m = 4 is correct! However, your working has some mistakes. In the first step you moved the divide by 13 to the wrong place: the whole expression should be divided by 13, not just the inner part. There are also sign errors in the second bracket. Try reworking it carefully to match your correct answer.
$\frac{5 [2 - (\frac{3 m + 1}{4} - \frac{m - 2}{5})]}{13} - \frac{3 (\frac{2 m + 3}{6} - (1 + \frac{m}{10}))}{11} = - \frac{43}{52}$
Your final answer m = 4 is correct, well done! However, in your first step you wrote (1 + m/10) instead of (1 - m/4) on the right side, and many middle steps are missing or unclear. Please show all your working more carefully so we can follow your reasoning from start to finish.
$\frac{5 (2 - (\frac{3 m + 1}{4} - \frac{m - 2}{5}))}{13} - \frac{3 (\frac{2 m + 3}{6} - (1 - \frac{m}{4}))}{11} = - \frac{43}{52}$
Your answer m = 4 is correct! When you substitute it back into the original equation, both sides equal the same value. Your working has some notation that is hard to follow in places, but you reached the right solution. Well done!

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