Question

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

Explanation:

1. First, solve the absolute - value inequality \(|2x - 6|\lt4\):

• Recall that if \(|u|\lt a\) (\(a\gt0\)), then \(-a\lt u\lt a\).
• For \(|2x - 6|\lt4\), we have \(-4\lt2x - 6\lt4\).
• Add 6 to all parts of the compound - inequality: \(-4 + 6\lt2x-6 + 6\lt4 + 6\).
• This simplifies to \(2\lt2x\lt10\).
• Divide all parts by 2: \(1\lt x\lt5\).

1. Then, analyze the number - line representation:

• The solution \(1\lt x\lt5\) is represented on a number line with an open circle at \(x = 1\) and an open circle at \(x = 5\), and the line segment between them is shaded.

Since the options are not labeled, we can't give a letter - based answer. But the correct number line has open circles at 1 and 5 and the segment between 1 and 5 shaded.

Answer:

A number line with open circles at 1 and 5 and the segment between 1 and 5 shaded.