Answered

IDNLearn.com: Your one-stop destination for reliable answers to diverse questions. Get the information you need from our community of experts, who provide detailed and trustworthy answers.

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 :

GinnyAnsweridn
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
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.