Graph the inequality on a number line.  Then write the solution in interval notation.

StartSet x|x greater than or equals 0.8 EndSet{x|x≥0.8}

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Part 1

Select the correct graph below.

A.

An infinite number line, labeled from negative 10 to 10 with tick marks in increments of 1. At 0.8, the shaded region starts with a left bracket and points to the right.-10-8-6-4-202468100.8

B.

An infinite number line, labeled from negative 10 to 10 with tick marks in increments of 1. At 0.8, the shaded region starts with a right bracket and points to the left.-10-8-6-4-202468100.8

C.

An infinite number line, labeled from negative 10 to 10 with tick marks in increments of 1. At 0.8, the shaded region starts with a left parenthesis and points to the right.-10-8-6-4-202468100.8

D.

An infinite number line, labeled from negative 10 to 10 with tick marks in increments of 1. At 0.8, the shaded region starts with a right parenthesis and points to the left.-10-8-6-4-202468100.8

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.

Graph the inequality on a number line. Then write the solution in interval notation. StartSet x|x greater than or equals 0.8 EndSet{x|x≥0.8}

Understand how to graph the inequality x ≥ 0.8 on a number line and express the solution using interval notation. This problem covers key concepts in inequalities, number line graphing, and interval notation, suitable for students in Grades 6-8.

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