Why is the line of the inequality solid when <= or >= and dotted when < or >?
It is a representation. If <=, the equal says the values can be on the line. If dotted, they cannot be on the line, but only < or > (ie, dotted means values on either side of the dotted line are allowed.)
The line of the inequality being solid or dotted is a way to visually represent the solution set of the inequality on a coordinate plane.
When the inequality symbol is either ≤ (less than or equal to) or ≥ (greater than or equal to), the line is drawn as a solid line. This is because the equal sign in the symbol indicates that the values on the line itself are included in the solution set. In other words, the points lying on the line satisfy the inequality.
On the other hand, when the inequality symbol is either < (less than) or > (greater than), the line is drawn as a dotted line. This is because there is no equal sign in these symbols, indicating that the values on the line itself are not included in the solution set. Instead, the points lying on either side of the dotted line satisfy the inequality.
To determine whether the line should be solid or dotted, you need to carefully consider the inequality symbol and whether the equal sign is present. If it is present, draw a solid line; if it is not present, draw a dotted line. This visual representation helps us understand which values are included in the solution set of the inequality.