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7/2x + 1/2x = 3x + 10/2 + 7/2x
Question: 7/2x + 1/2x = 3x + 10/2 + 7/2x
Is the problem suppose to be 7x/2 + x/2 = 3x + 10/2 + 7x/2?
I've gotten us to several questions having 7/2x meaning 7/(2x),
but I don't feel that this one reads that way. Just for fun,
I'll do it that way
Lets put all terms over 2 by multiplying those not over 2 by 2/2.
This gives 7x/2 + x/2 = 6x/2 + 10/2 + 7x/2.
The entire equation can now be multiplied by 2. The result is
7x + x = 6 + 10 + 7x.
Note that 7x on both sides can be cancelled, leaving only x = 6x + 10.
Subtract 6x from both sides and the result is 5x = 10.
Divide both sides by 5 and the result is x = -2.
To check this out, put it back in the equation at top, giving
(7/2)(-2) + (1/2)(-2) = 3(-2) + 10/2 + (7/2)(-2).
This reduces to 7 1 = -6 + 5 7, which is 8 = 8.
That looks like it to me...
If you want to, read on!
Now just for fun, let's suppose that x were on the bottom of the fractions. We would start by multiplying the entire equation by 2x.
That would give 7 + 1 = 6x² + 10x + 7.
Subtracting 8 from both sides would give 0 = 6x² + 10x - 1.
Now if that were the case (but I don't think it is),
you would get an expression for x involving √124 = 2√31,
but usually basic math has very simple answers.
The exact answer would be (-10 ± 2√31)/12 = (-5 ± √31)/6.
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Scott A Wilson
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