Answer
$x=\left\{ -4,\dfrac{17}{3} \right\}$
Work Step by Step
Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $
|5-6x|=29
$ evaluates to
\begin{array}{l}
5-6x=29\\
-6x=24\\
x=-4
,\\\\\text{OR}\\\\
5-6x=-29\\
-6x=-34\\\\
x=\dfrac{34}{6}\\\\
x=\dfrac{17}{3}
.\end{array}
Hence, the solution set is $
x=\left\{ -4,\dfrac{17}{3} \right\}
$.
