Question

1. higher order thinking it is given that |a| = |b|. can you conclude that a = b? explain your reasoning.

Explanation:

Step1: Recall absolute - value definition

The absolute value of a number \(x\), denoted as \(|x|\), is defined as \(|x|=

$$\begin{cases}x, & x\geq0\\ - x, & x < 0\end{cases}$$

\).

Step2: Consider cases

If \(|a| = |b|\), we have two cases. Case 1: \(a = b\) (for example, if \(a = 3\) and \(b = 3\), then \(|3|=|3| = 3\)). Case 2: \(a=-b\) (for example, if \(a = 3\) and \(b=-3\), then \(|3|=| - 3| = 3\)).

Answer:

No. Because \(|a| = |b|\) can mean \(a = b\) or \(a=-b\).