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What is the solution, if any, to the inequality [tex]|3x| \geq 0[/tex]?

A. all real numbers
B. no solution
C. [tex]x \geq 0[/tex]
D. [tex]x \leq 0[/tex]

Sagot :

GinnyAnswer
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
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