Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

For which value of k does the function below have only one real solution? Use the format k=.. for your response?

|4 + 7x| -15 < k

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  • 1 month ago
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    The absolute value will result in a non-zero value (0 or greater).

    Then when you subtract -15, you'll get a value of -15 or greater.

    In order to restrict that to a single value, the only choice is if you were looking for -15 exactly.

    In other words, it would only return a single value if the sign were less than or equal to (≤) and k = -15.

    |4 + 7x| - 15 ≤ -15

    But the inequality symbol is less than (<). There is no way to pick just one single number that is bigger than -15. And also, you would end up having *two* values any way that would equal that result.

    Answer:

    If the symbol were changed to ≤, then the answer would be k = -15. But as written there is no value of k that will work.

  • 1 month ago

    No value of k can give this a single real solution. 

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