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# 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.

### 3 Answers

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- JohnathanLv 72 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 72 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

- az_lenderLv 72 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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