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Q: If the ratio of 4a to 3b is 8 to 9 what is the ratio of 3a to 4b?
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What is the equivalent to 3a plus 4b - -6a - 3b?

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Clearly, there are some signs missing. So let's try the four possibilities for the second terms: 1. + and + 3a + 4b = 7a + 4b Subtract 4b from each side: 3a = 7a Subtract 3a from each side: 0 = 4a Answer : a = 0, b indeterminate (ie can have any vaue). 2. + and - 3a + 4b = 7a - 4b Subtract 4b from each side: 3a = 7a - 8b Subtract 7a from each side: -4a = -8b or 4a = 8b Answer: a = 2b 3. - and - 3a - 4b = 7a - 4b Add 4b to each side: 3a = 7a Subtract 3a from each side: 0 = 4a Answer : a = 0, b indeterminate (ie can have any vaue). 4. - and + 3a - 4b = 7a + 4b Add 4b to each side: 3a = 7a + 8b Subtract 7a from each side: -4a = 8b or 4a = -8b Answer: a = -2b Can't do better than that with the information available.


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(5a - 4b) + (2c - 3b - 6c) + a =5a - 4b + 2c - 3b - 6c + a =(5a + a) + (-4b - 3b) + (2c - 6c) =[ 6a - 7b - 4c ].


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