The inequality given is $x \geq 0.8$, which means $x$ is greater than or equal to 0.8. Let's break this down for the graph and the interval notation:

Graph Explanation:

• Since $x \geq 0.8$, we need to shade the portion of the number line starting at 0.8 and continuing to the right (towards larger numbers).
• The symbol "greater than or equal to" ( $\geq$ ) means that 0.8 is included in the solution set, so we will use a closed bracket ( [ ) at 0.8.

Solution in Interval Notation:

• The solution is all numbers from 0.8 to infinity, including 0.8.
• Therefore, in interval notation, the solution is: $[0.8, \infty)$

Correct Graph:

• The correct graph will have a closed bracket at 0.8, with the shaded region extending to the right.

Answer:

The correct graph is Option A:

• A number line with a left bracket at 0.8, and shading towards the right (positive direction).

Do you want further details on how interval notation works or how to interpret inequalities?

Here are 5 questions to expand your understanding:

1. What would the graph look like if the inequality was $x > 0.8$?
2. How would the interval notation change if $x$ was strictly greater than 0.8?
3. What happens if we reverse the inequality, say $x \leq 0.8$?
4. Can you graph a double inequality like $0.8 \leq x \leq 5$?
5. How would you represent $x > -5$ on the number line and in interval notation?

Tip: When dealing with "greater than or equal to" ( $\geq$ ), always use a closed bracket or filled dot to indicate that the boundary point is included in the solution set.