what is the solution, if any, to the inequality |3x|≥0?\nall real numbers\nno solution\nx≥0\nx≤0
what is the solution, if any, to the inequality |3x|≥0?\nall real numbers\nno solution\nx≥0\nx≤0
Answer
Explanation:
Step1: Recall absolute - value property
The absolute - value of any real number (a), denoted as (|a|), is defined as (|a|=\begin{cases}a, & a\geq0\-a, & a < 0\end{cases}), and (|a|\geq0) for all real numbers (a). Let (a = 3x). Since the absolute - value of any real number is always non - negative, for any real number (x), the value of (|3x|) is either zero (when (x = 0)) or positive (when (x\neq0)).
Step2: Determine the solution set
The inequality (|3x|\geq0) is true for all real values of (x) because the absolute - value function (y = |3x|) will always return a non - negative value.
Answer:
all real numbers