Question

What are the two possible answers for the equation Ix/5I = 3?

Answer 1

Either
`x = -15` or
`x = 15`.

Explanation:

`|x| = \left\lbrace \begin{aligned} & x && \text{if $x \ge 0$} \\ & -x && \text{if $x < 0$}\end{aligned}\right.`.

Hence, there are two possibilities to consider:

• Either
  `(x / 5) \ge 0`,
• Or
  `(x / 5) < 0`.

If
`(x / 5) \ge 0`, then
`|x / 5| = x / 5`.

Substitute into the original equation:
`x/ 5= 3`. Solve for
`x`:
`x = 15`.

Important: verify that the solution
`x = 15` meet the assumption
`(x / 5) \ge 0`. Indeed,
`(x / 5) = (15 / 5) = 3` and is indeed non-negative. Hence, the solution
`x = 15\!` is valid.

On the other hand, if
`(x / 5) < 0`, then
`|x / 5| = - x / 5`.

Substitute into the original equation:
`(-x / 5) = 3`. Solve for
`x`:
`x = -15`.

Similarly, verify that the solution
`x= - 15` satisfies the current assumption that
`(x / 5) < 0`. Indeed, this assumption is met, and
`x = -15` is also a valid solution.