Question

1. | - 2x + 3| > - 4

Explanation:

Step1: Recall property of absolute value

The absolute - value of any real number \(y\), denoted as \(|y|\), is always non - negative, i.e., \(|y|\geq0\) for all real numbers \(y\). In the inequality \(|-2x + 3|>-4\), since \(|-2x + 3|\geq0\) for all real values of \(x\), and \(0>-4\).

Step2: Determine the solution set

Because the absolute - value \(|-2x + 3|\) is always greater than or equal to \(0\), it is always greater than \(-4\) for all real values of \(x\). So the solution set is all real numbers.

Answer:

\(x\in(-\infty,\infty)\)