To solve the inequality [tex]\( |3x| \geq 0 \)[/tex], let's break it down step-by-step:
1. Understanding Absolute Value: The absolute value of a number [tex]\( |a| \)[/tex] is defined as the distance of [tex]\( a \)[/tex] from zero on the number line, regardless of direction. Therefore, [tex]\( |a| \)[/tex] is always non-negative, that is, [tex]\( |a| \geq 0 \)[/tex] for all real numbers [tex]\( a \)[/tex].
2. Applying Absolute Value to the Inequality: In the given inequality, we have [tex]\( |3x| \)[/tex]. The expression [tex]\( |3x| \)[/tex] represents the absolute value of [tex]\( 3x \)[/tex], which means it will always be non-negative. Therefore, [tex]\( |3x| \geq 0 \)[/tex].
3. Analyzing the Inequality: Since [tex]\( |3x| \)[/tex] represents the absolute value of [tex]\( 3x \)[/tex] and absolute values are always greater than or equal to 0, the inequality [tex]\( |3x| \geq 0 \)[/tex] will always hold true no matter what value [tex]\( x \)[/tex] takes.
4. Conclusion: Given the nature of absolute values, the inequality [tex]\( |3x| \geq 0 \)[/tex] is satisfied for all real numbers [tex]\( x \)[/tex]. There are no exceptions or special conditions required for [tex]\( x \)[/tex] to satisfy this inequality.
Therefore, the solution to the inequality [tex]\( |3x| \geq 0 \)[/tex] is:
All real numbers
