The number line is very important for understanding linear inequalities, especially in Gymnasium Year 1 math. It helps students visualize what inequalities mean and find their solutions. Here are some key points about the number line:

1. Seeing Inequalities: The number line lets students see inequalities like ( x < 5 ) or ( x \geq 2 ) in a simple way. For ( x < 5 ), students can shade the part of the line to the left of 5. This shows all the numbers that are less than 5.

2. Finding Solutions: Each inequality has a set of solutions that can be shown on the number line. For example:

   • For ( x > -1 ), all numbers greater than -1 are part of the solution.
   • For ( x \leq 3 ), the shaded area includes 3 and all the numbers less than 3.

3. Important Points: When solving inequalities, students learn to find important points (the numbers where the inequality changes). For example, in the inequality ( x - 2 < 3 ), the important point is ( x = 5 ). This helps students find the solution set.

4. Combining Solutions: The number line also helps show how different inequalities overlap or combine. For instance, the solution to the inequality ( 2 < x < 5 ) can be shown by shading the part of the line between 2 and 5.

In summary, the number line is a key tool for solving linear inequalities. It helps students see and understand the solution sets in a clearer way.