Answer:
1/8(7x +2) +3x = 4x +9
Explanation:
The value of x will be smallest when it is most negative. Here, that will occur when the numerator of the rational solution for x is as large a positive number as possible, and the denominator is a small negative number.
If we call the spaces a, b, ..., g, then the value of x is ...
x = (bg -ad)/(ac +b(e-f))
This is smallest (most negative) when bg is as large as possible (8·9), and ad is as small as possible (1·2). Then values for c, e, f can be chosen to make the denominator -1. The solution for x looks like ...
x = (8·9 -1·2)/(1·7 +8(3 -4)) = 70/-1 = -70
The smallest possible value of x is -70. One way to obtain that value is ...
1/8(7x +2) +3x = 4x +9
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There are numerous ways to obtain "indeterminate" results where the equation reduces to one with no solution. And there are a number of ways to have the solution be infinity: (ac-b(e-f)) = 0.