Answer
no solution
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
12+8|3d-8|\le10
,$ 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}
12+8|3d-8|\le10
\\\\
8|3d-8|\le10-12
\\\\
8|3d-8|\le-2
\\\\
|3d-8|\le-\dfrac{2}{8}
\\\\
|3d-8|\le-\dfrac{1}{4}
.\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 $\text{
no solution
.}$
