Certainly! Let's interpret and express the given solution in interval notation step by step.
1. Interval Notation Interpretation:
- The interval is given as [tex]\((2, \infty)\)[/tex].
- This means that we are considering all numbers greater than 2 but not including 2 itself.
- The interval starts just after 2 and extends endlessly in the positive direction.
2. Understanding the Interval:
- A notation of the form [tex]\( (a, b) \)[/tex] typically means [tex]\( a < x < b \)[/tex].
- Here, [tex]\(a = 2\)[/tex] and [tex]\(b = \infty\)[/tex], so [tex]\( 2 < x < \infty \)[/tex].
- The number 2 is not included in the interval, which is why we use a parenthesis instead of a bracket.
3. Inequality Form:
- In inequality form, this can be expressed as [tex]\( x > 2 \)[/tex].
- This directly translates the idea that [tex]\( x \)[/tex] can be any number greater than 2.
4. In Words:
- You might describe the solution set as: "The set of all numbers greater than 2."
So, to summarize, another way to express the solution [tex]\((2, \infty)\)[/tex] in words or another mathematical form is:
[tex]\[ x > 2 \][/tex]
This clearly indicates that the number we are looking for must be any value strictly greater than 2.
