## College Algebra (11th Edition)

$(-\infty, \infty)$
$\bf{\text{Solution Outline:}}$ 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 $(-\infty, \infty) .$