#### Answer

$(-\infty,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the concepts of absolute value expressions to solve the given inequality, $ |12-9x|\ge-12 .$
$\bf{\text{Solution Details:}}$
The absolute value of a number is the distance of the number from $0,$ and hence, is always a nonnegative number. In the same reason, for any $x$, the expression at the left side is always a nonnegative number. This will always be $\text{ greater than or equal to }$ the expression at the right. Hence, the solution is the set of all real numbers or $
(-\infty,\infty)
.$