Question

4 a. explain what the solutions to the inequality |x - 4.26| ≥ 0 mean based on distance on a number line. what are the solutions? all the numbers are solutions

Explanation:

Step1: Recall the definition of absolute value

The absolute value \(|a|\) represents the distance of \(a\) from \(0\) on the number line. In the expression \(|x - 4.26|\), it represents the distance of \(x\) from \(4.26\) on the number line.

Step2: Analyze the inequality \(|x - 4.26|\geq0\)

Since distance is always non - negative (i.e., distance \(d\geq0\) for any two points on the number line). The distance of \(x\) from \(4.26\) (which is \(|x - 4.26|\)) is always greater than or equal to \(0\) for all real values of \(x\).

Answer:

The solutions to the inequality \(|x - 4.26|\geq0\) mean that all real numbers \(x\) satisfy the inequality. Because the absolute value of a number (in this case, the distance of \(x\) from \(4.26\) on the number line) is always non - negative. The set of solutions is \(x\in(-\infty,\infty)\) (all real numbers).