Answer
no solution
Work Step by Step
$\bf{\text{Solution Outline:}}$
Isolate first the absolute value expression in the given equation, $
-2|d-8|+1=11
.$ Then use the definition of absolute value to analyze the solution.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
-2|d-8|+1=11
\\\\
-2|d-8|=11-1
\\\\
-2|d-8|=10
\\\\
\dfrac{-2|d-8|}{-2}=\dfrac{10}{-2}
\\\\
|d-8|=-5
.\end{array}
The absolute value of $x,$ given as $|x|,$ is the distance of $x$ from $0.$ Hence, it is a nonnegative number. In the same way, the left side of the equation above is always a nonnegative number. This will never be equal to the negative number at the right side. Hence, there is $\text{
no solution
.}$
