Cool Down
For questions 1–3, use the following scenario to write inequalities and to identify solutions.
Here is another riddle:
- The sum of two numbers is less than 2.
- If we subtract the second number from the first, the difference is greater than 1.
What are the two numbers?
1.
The riddle can be represented by a system of inequalities. Write an inequality for each statement.
Compare your answer:
2.
![Graph of a system of two linear inequalities on a coordinate plane.]()
These graphs represent the inequalities in the system.
Compare your answer: Your answer may vary, but here is a sample.
The region with solid blue shading represents the first clue. The region with line shading represents the second clue.
3.
Name a possible solution to the riddle. Explain or show how you know.
Compare your answer: Your answer may vary, but here are some samples.
- (1.5, 0). The sum is 1.5, which is less than 2. The difference is 1.5, which is greater than 1. The point (1.5, 0) is located in the region where the two shaded regions overlap, which means it is a solution to both inequalities in the system.
- (2, -1). The sum is 1, which is less than 2. The difference is 3, which is greater than 1. The point (2, -1) is located in the region where the two shaded regions overlap, which means it is a solution to both inequalities in the system.