Answer
Solution set: $(-\infty,\infty).$
Work Step by Step
Follow the "Procedure for Solving Polynomial lnequalities",\ p.412:
1. Express the inequality in the form
$f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$
where $f$ is a polynomial function.
$4x^{2}-4x+1\geq 0$
We recognize the LHS as a square of a difference...
$(2x-1)^{2} \geq 0$
...
We do not need to follow the steps any further, since this inequality asks:
"For which real numbers is a square nonnegative?"
The answer: "Always (for all x$\in \mathbb{R}$)."
Solution set: $(-\infty,\infty).$
