Question

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

Answer 1

Answer:

Either $x = -15$ or $x = 15$.

Step-by-step 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.