Answer:
Either [tex]x = -15[/tex] or [tex]x = 15[/tex].
Step-by-step explanation:
[tex]|x| = \left\lbrace \begin{aligned} & x && \text{if $x \ge 0$} \\ & -x && \text{if $x < 0$}\end{aligned}\right.[/tex].
Hence, there are two possibilities to consider:
If [tex](x / 5) \ge 0[/tex], then [tex]|x / 5| = x / 5[/tex].
Substitute into the original equation: [tex]x/ 5= 3[/tex]. Solve for [tex]x[/tex]: [tex]x = 15[/tex].
Important: verify that the solution [tex]x = 15[/tex] meet the assumption [tex](x / 5) \ge 0[/tex]. Indeed, [tex](x / 5) = (15 / 5) = 3[/tex] and is indeed non-negative. Hence, the solution [tex]x = 15\![/tex] is valid.
On the other hand, if [tex](x / 5) < 0[/tex], then [tex]|x / 5| = - x / 5[/tex].
Substitute into the original equation: [tex](-x / 5) = 3[/tex]. Solve for [tex]x[/tex]: [tex]x = -15[/tex].
Similarly, verify that the solution [tex]x= - 15[/tex] satisfies the current assumption that [tex](x / 5) < 0[/tex]. Indeed, this assumption is met, and [tex]x = -15[/tex] is also a valid solution.
