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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    Multiply both sides by 4(x+7)

  2. anonymous
    • 5 years ago
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    I did but that led me to x^2-9x+172 and that doesnt seem right

  3. anonymous
    • 5 years ago
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    \[x(x+7) + 4(15) \le 4*4(x+7)\] \[\implies x^2 + 7x + 60 \le 16x + 112\] \[\implies x^2 -9x - 52 \le 0\]

  4. anonymous
    • 5 years ago
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    So solve the quadratic for 0 and you have your solutions.

  5. anonymous
    • 5 years ago
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    I got -9 and 13......how do I use those to find the domain?

  6. anonymous
    • 5 years ago
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    that is the domain

  7. anonymous
    • 5 years ago
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    its an inequality theres a different way to solve for the domain

  8. anonymous
    • 5 years ago
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    No, factor it.

  9. anonymous
    • 5 years ago
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    \[(x -13)(x+4) \le 0\]

  10. anonymous
    • 5 years ago
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    That means that one of those two factors must be negative (but not both) for the relation to hold.

  11. anonymous
    • 5 years ago
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    So what values of x will yield a negative in one of either (x-13) or (x+4) but not both.

  12. anonymous
    • 5 years ago
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    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)

  13. anonymous
    • 5 years ago
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    If x is between -4 and 13 (say maybe x=0) we have one positive and one negative, so that seems reasonable.

  14. anonymous
    • 5 years ago
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    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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