#### Answer

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
20+3|5x-2|\le11
,$ 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}
20+3|5x-2|\le11
\\\\
3|5x-2|\le11-20
\\\\
3|5x-2|\le-8
\\\\
|5x-2|\le-\dfrac{8}{3}
.\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 always a nonnegative number. This is never $\text{
less than or equal to
}$ the negative number at the right. Hence, there is $\text{
no solution
.}$