Answer
all real numbers
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-6|p-4|+3\le16
,$ isolate first the absolute value expression. Then use the definition of absolute value to analyze the solution.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
-6|p-4|\le16-3
\\\\
-6|p-4|\le13
\\\\
\dfrac{-6|p-4|}{-6}\ge\dfrac{13}{-6}
\\\\
|p-4|\ge-\dfrac{13}{6}
.\end{array}
The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from zero. Hence, it is always a nonnegative number. In the same way, the left side of the inequality above is a nonnegative number. This is always $\text{
greater than or equal to
}$ the negative number at the right. Hence, the solution is the set of $\text{
all real numbers
.}$
