Answer
Solution set = $\displaystyle \{-\frac{4}{5}, 4\}$
Work Step by Step
$ 2\displaystyle \left| 4-\frac{5}{2}x\right|+6=18\qquad$ ... subtract 6
... isolate the absolute value bracket
$ 2\displaystyle \left| 4-\frac{5}{2}x\right|=12\qquad$ ... divide with 2
$\displaystyle \left| 4-\frac{5}{2}x\right|=6\qquad$ ... remove absolute value
$\left.\begin{array}{cccclll}
4-\frac{5}{2}x=6 & /\times 2 & or & 4-\frac{5}{2}x=-6 & /\times 2\\
8-5x=12 & /-8 & & 8-5x=-12 & /-8\\
-5x=4 & /\div(-5) & & -5x=-20 & /\div(-5)\\
x=-4/5 & & & x=4 &
\end{array}\right.$
Solution set = $\displaystyle \{-\frac{4}{5}, 4\}$
