Question
If you were to graph and inequality on a number line, say, m>=10 or m<=9, would the lines be touching or facing in different directions?
Answers
Answered by
GPT-4o mini
When graphing the inequalities \( m \geq 10 \) and \( m \leq 9 \) on a number line, you would represent them as follows:
1. **For \( m \geq 10 \)**:
- You would place a solid dot (or a filled circle) at 10 to indicate that 10 is included in the solution (because of the "greater than or equal to" part).
- Then you would shade the line to the right of 10, indicating all values greater than 10.
2. **For \( m \leq 9 \)**:
- You would place a solid dot at 9 to indicate that 9 is included in the solution (because of the "less than or equal to" part).
- Then you would shade the line to the left of 9, indicating all values less than 9.
Since the two inequalities \( m \geq 10 \) and \( m \leq 9 \) do not overlap (there are no numbers that can satisfy both inequalities simultaneously), the lines will be facing in different directions. Specifically, the shaded region for \( m \geq 10 \) would extend to the right, while the shaded region for \( m \leq 9 \) would extend to the left. Thus, they do not touch each other on the number line.
1. **For \( m \geq 10 \)**:
- You would place a solid dot (or a filled circle) at 10 to indicate that 10 is included in the solution (because of the "greater than or equal to" part).
- Then you would shade the line to the right of 10, indicating all values greater than 10.
2. **For \( m \leq 9 \)**:
- You would place a solid dot at 9 to indicate that 9 is included in the solution (because of the "less than or equal to" part).
- Then you would shade the line to the left of 9, indicating all values less than 9.
Since the two inequalities \( m \geq 10 \) and \( m \leq 9 \) do not overlap (there are no numbers that can satisfy both inequalities simultaneously), the lines will be facing in different directions. Specifically, the shaded region for \( m \geq 10 \) would extend to the right, while the shaded region for \( m \leq 9 \) would extend to the left. Thus, they do not touch each other on the number line.