#### Answer

$(-\infty, \infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|4x-12|\ge-3
,$ use the definition of absolute value to analyze the given inequality.
$\bf{\text{Solution Details:}}$
The absolute value of $x$, given by $|x|,$ is the distance of $x$ from $0,$ and hence is always a nonnegative number. Therefore, for any $x,$ the expression at the left, $
|4x-12|
,$ is nonnegative. This is always greater than or equal to the negative expression at the right. Hence, the solution set is the set of all real numbers or the interval $
(-\infty, \infty)
.$