SOLUTION: Solve the polynomial inequality. Express the solution set in interval notation. 4x^2 + 1 is greater than or equal to 4x

 >= .    (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 (, ).