Solve the inequality x 15 --- + ---- <= 4 4 x+7 for domain

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Solve the inequality x 15 --- + ---- <= 4 4 x+7 for domain

Mathematics
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Multiply both sides by 4(x+7)
I did but that led me to x^2-9x+172 and that doesnt seem right
\[x(x+7) + 4(15) \le 4*4(x+7)\] \[\implies x^2 + 7x + 60 \le 16x + 112\] \[\implies x^2 -9x - 52 \le 0\]

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Other answers:

So solve the quadratic for 0 and you have your solutions.
I got -9 and 13......how do I use those to find the domain?
that is the domain
its an inequality theres a different way to solve for the domain
No, factor it.
\[(x -13)(x+4) \le 0\]
That means that one of those two factors must be negative (but not both) for the relation to hold.
So what values of x will yield a negative in one of either (x-13) or (x+4) but not both.
between -4 and 13? my options for an answer are A. (-7,-4] U [13, inf) B. (-inf,-7)U(-4,13) C. (-inf,-7]U[-4,13) D. (-inf,-7)U[-4,13] E. (-7,-4)U(13,inf)
If x is between -4 and 13 (say maybe x=0) we have one positive and one negative, so that seems reasonable.
We did get rid of a factor of x+7 though when we solved it, so I think your answer is probably D.

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