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anonymous

  • 5 years ago

can you help me to solve the following inequality: x^2 >=16

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  1. anonymous
    • 5 years ago
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    Can you show the work, please?

  2. anonymous
    • 5 years ago
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    graph \[y=x^2-16\] and you will see a parabola that faces up and crosses the x-axis at -4 and 4. from the picture you will see that it is positive if x<-4 or if x> 4

  3. anonymous
    • 5 years ago
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    analitically

  4. anonymous
    • 5 years ago
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    there is another more complicated way to do this, but if you know what the graph of \[y=x^2-16\] looks like it is simple.

  5. anonymous
    • 5 years ago
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    well step number one is going to be to write \[x^2-16\geq0\]

  6. anonymous
    • 5 years ago
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    so you are going to have to work with that in any case. you cannot, for example, take the square root of both sides.

  7. anonymous
    • 5 years ago
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    I need to do it analitically

  8. anonymous
    • 5 years ago
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    then you can factor \[x^2-16=(x+4)(x-4)\geq 0\]

  9. anonymous
    • 5 years ago
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    got it

  10. anonymous
    • 5 years ago
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    Im such a fool

  11. anonymous
    • 5 years ago
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    then you can look at the sign of each factor. yes?

  12. anonymous
    • 5 years ago
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    you are still going to get positive, negative, positive on \[(-\infty,-4), (-4,4), (4,\infty) \] respectively

  13. anonymous
    • 5 years ago
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    thanks

  14. anonymous
    • 5 years ago
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    welcome

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