Find the interval on the real number line for which the radicand is nonnegative. (4th root of)(5-7x)?

Please explain how to find the interval of things.

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3 Answers

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  • 2 years ago

    Just set 5 - 7x >= 0 and solve for x as normal, since anything that is non-negative cannot be less than 0.

  • ?
    Lv 7
    2 years ago

    ∜(5-7x) ≧ 0

    // Raise both sides to the 4th power

    [∜(5-7x)]⁴ ≧ [0]⁴

    5-7x ≥ 0

    // Now solve for x

    -7x ≥ -5

    x ≤ ⁵⁄₇

    // Therefore, the interval is

    x ≤ ⁵⁄₇, written (-∞,⁵⁄₇]..............ANS

  • 2 years ago

    The "radicand" is the expression 5-7x, the quantity under the radical sign.

    This will be non-negative if 5 >= 7x, in other words if x <= 5/7.

    As an "interval," this would be expressed as (-infinity, +5/7].

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