edmundo used a number line to show the solution for the inequality |2x - 6| < 4. which number line shows the…

Explanation:

Step1: Remove absolute - value

If (|a|\lt b) ((b > 0)), then (-b\lt a\lt b). So for (|2x - 6|\lt4), we have (-4\lt2x - 6\lt4).

Step2: Add 6 to all parts

Adding 6 to each part of the compound - inequality (-4\lt2x - 6\lt4) gives (-4 + 6\lt2x-6 + 6\lt4 + 6), which simplifies to (2\lt2x\lt10).

Step3: Divide by 2

Dividing each part of (2\lt2x\lt10) by 2, we get (\frac{2}{2}\lt\frac{2x}{2}\lt\frac{10}{2}), or (1\lt x\lt5). The solution on the number - line is an open interval from 1 to 5.

Answer:

The number - line with an open circle at 1, an open circle at 5, and a line segment connecting them (the first option among the given ones where the line segment is between 1 and 5 with open circles at 1 and 5).