To solve the inequality [tex]\(\sqrt{x} > 2\)[/tex], let's go through the steps systematically:
1. Understand the Inequality:
The inequality [tex]\(\sqrt{x} > 2\)[/tex] means that the square root of [tex]\(x\)[/tex] must be greater than 2.
2. Square Both Sides:
To remove the square root, square both sides of the inequality. Remember, squaring is a monotonic function when dealing with non-negative numbers, so it preserves the direction of the inequality.
[tex]\[
(\sqrt{x})^2 > 2^2
\][/tex]
[tex]\[
x > 4
\][/tex]
3. Interpret the Solution:
The inequality [tex]\(x > 4\)[/tex] tells us that [tex]\(x\)[/tex] must be any number greater than 4. In interval notation, this can be written as:
[tex]\[
(4, \infty)
\][/tex]
4. Identify the Graph of the Inequality:
Now, consider the solution on the number line and the type of graphs that represent inequalities of this form. A graphical representation of [tex]\(x > 4\)[/tex] typically has an open circle at 4 and shading to the right, indicating all numbers greater than 4.
So, you would look at the provided graphs (not shown here) and find the one that matches an open circle at [tex]\(x = 4\)[/tex] and a shaded region to the right of 4. Based on this description, you can determine the correct graph.
Since the exact diagrams are not provided in your question, you should match this description to the choices given. The correct answer is the graph that visually represents [tex]\(x > 4\)[/tex].
Would you like me to proceed based on assumptions about possible options, or do you have details about the graphs that I could use?
