To determine the solution to the inequality [tex]\(|3x| \geq 0\)[/tex], let's go through a detailed step-by-step analysis.
1. Understanding Absolute Value: The absolute value of a number is always non-negative. This means that for any real number [tex]\(y\)[/tex], [tex]\(|y| \geq 0\)[/tex].
2. Applying Absolute Value Properties: Given the inequality [tex]\(|3x| \geq 0\)[/tex], we recognize that the absolute value of [tex]\(3x\)[/tex] will always be a non-negative number.
- [tex]\(|3x|\)[/tex] represents the distance of [tex]\(3x\)[/tex] from zero on the number line.
- Since distance cannot be negative, [tex]\(|3x|\)[/tex] is always greater than or equal to zero, regardless of the value of [tex]\(x\)[/tex].
3. Solving the Inequality:
- Because [tex]\(|3x|\)[/tex] will always be non-negative for any real number [tex]\(x\)[/tex], it automatically satisfies the inequality [tex]\(|3x| \geq 0\)[/tex].
4. Conclusion: Since there are no restrictions on [tex]\(x\)[/tex] that would make the inequality false, the inequality holds for all real numbers.
Thus, the solution to the inequality [tex]\(|3x| \geq 0\)[/tex] is [tex]\(\boxed{\text{all real numbers}}\)[/tex].
