A moderate person takes in 2400 to 2800 calories. Draw a graph on a number line and write a compound inequality for the graph.
Well, breaking out my artistic skills here, I present to you a graph on a number line:
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Great, now let's formulate a compound inequality for this graph. Since a moderate person takes in 2400 to 2800 calories, we can set up our inequality as:
2400 ≤ x ≤ 2800
Here, 'x' represents the number of calories. So, according to our magical graph, the person's calorie intake falls between 2400 and 2800 calories.
To graph the number line, we will plot the values 2400 and 2800, representing the range of calories for a moderate person.
1. Draw a horizontal line and label it with a scale from 0 to 3000 (or any suitable range for the graph).
```
0────────┬─────────┬─────────┬───────┬─────────┬───────┬───────┬─────►
1000 2000 2400 2600 2800 3000
```
2. Mark a point at the value 2400.
3. Mark another point at the value 2800.
```
0────────┬─────────┬─────────┬───────┬─────────┬───────┬───────┬─────►
1000 2000 2400 2600 2800 3000
● ○
```
Now, to write a compound inequality for the graph:
Let x be the number of calories a person takes in.
The compound inequality for a moderate person taking in 2400 to 2800 calories can be written as:
2400 ≤ x ≤ 2800
This represents that the number of calories a person takes in should be greater than or equal to 2400 and less than or equal to 2800.
To draw a graph on a number line and write a compound inequality for the given situation, follow these steps:
1. Determine the range of values on the number line: The number line should range from the minimum calories intake (2400) to the maximum calories intake (2800).
2. Mark the minimum value (2400) on the number line: Draw a point on the number line to represent 2400.
3. Mark the maximum value (2800) on the number line: Draw another point on the number line to represent 2800.
4. Connect the two points on the number line: Use a straight line to connect the points representing 2400 and 2800.
5. Write the compound inequality for the graph: In this case, the compound inequality can be written as follows:
2400 ≤ x ≤ 2800
This compound inequality represents the range of values where x (calories intake) is between or equal to 2400 and 2800, indicating a moderate person's calorie intake.