Question

which of the following is the solution to $|13x| > -5$?

a. $x < \frac{5}{13}$ or $x > -\frac{5}{13}$

b. $x > -\frac{5}{13}$

c. no solution

d. all values are solutions

Explanation:

Step1: Recall the property of absolute value

The absolute value of any real number \(|a|\) is always non - negative, i.e., \(|a|\geq0\) for all real numbers \(a\). In the given inequality \(|13x|>- 5\), since \(|13x|\) is always greater than or equal to \(0\) for any real number \(x\) (because the absolute value of a number represents its distance from \(0\) on the number line, and distance is non - negative), and \(0>-5\).

Step2: Determine the solution set

This means that for any real number \(x\), the inequality \(|13x|>-5\) will hold true. So the solution set of the inequality \(|13x|>-5\) is all real numbers.

Answer:

D. All values are solutions