Russ P. answered • 10/30/14

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Kayla,

Let n = unknown number, then your problem states that

2(n - 9) = 3(n + 6), so 2n-18 = 3n +18, and n = -36 ; Now check it: 2(-45)=3(-30) so this solution works.

But the statement "the difference of a number and 9" could also be interpreted as (9 - n). So we get a new equation:

2(9 - n) = 3(n + 6), where 18 - 2n = 3n + 18, so n = 0 becomes the solution. Check it: 2(9) = 3(6) so it also works.

Therefore, the ambiguity in the wording of the problem leads to two possible solutions: n=0 and n=-36.

Of course, you can interpret correctly the phrase as |n - 9|, and then this resolves into the 2 equations above since

|n - 9| = +(n - 9) and = -(n - 9) = (9 - n). Then the sing;e formula would have been 2|n - 9| = 3(n + 6). The answers are still the same as before.