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Solve the polynomial inequality. Express the solution set in interval notation.
4x^2 + 1 is greater than or equal to 4x
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>= . (1)
This inequality is equivalent to
>= .
Left side is . So the inequality takes the form
>= .
The last inequality is true for any x, because its left side is always non-negative as the square of real number (2x-1).
Therefore, the original equation (1) is valid for all real numbers x.
Thus the set of solutions to inequality (1) is all real numbers, the entire number line (, ).