Calculus/Pre-calc

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Expert: - 6/6/2009


Question
Find all the real solutions, if any, of the following
equation.

4x-5/3-7x=4

okay, i solved it and got 17/32. i just want to make sure if
this correct.
thanks !

Answer
The easiest way to do that is put it back into the equation.
Take x = 17/32, and put into (4x-5)(3-7x) and see if the answer is 4.

4*17/32 = 17/8.  5 is the same as 40/8.
So we have (17-40)/8 in the top.
That is, -23/8.

3 is 96/32.  7*17/32 = 119/32.
So we have (96-119)/32 in the bottom.
That is, -23/32.

Invert and multiply, giving (-23/8)(32/-23) = 32/8 = 4.

Looks right to me.  Look right to you?

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