The graphs of "x is less than or equal to 6" and "x is less than 6" differ in one key aspect: the inclusion of the point x = 6.
The graphs of x≤6 and x<6 represent different sets of solutions on the number line, and the key distinction lies in the inclusion or exclusion of the boundary value, in this case, x<6:
This graph represents all values of
x that are strictly less than 6.
The shaded region extends to the left of 6, covering all real numbers smaller than 6.
An open circle is placed at x=6 to indicate that 6 is not included in the solution set. The circle emphasizes that the boundary point is excluded. x≤6:
This graph includes all values of x that are less than or equal to 6.
The shaded region also extends to the left of 6, covering all real numbers less than 6.
A solid circle is placed at x=6 to indicate that 6 is included in the solution set. The solid circle emphasizes that the boundary point is included.
In summary, the primary difference is in the treatment of the boundary value.
In x<6, 6 is strictly excluded, while in x≤6, 6 is included as part of the solution set.
The choice between an open circle and a solid circle at the boundary point is crucial in conveying this distinction visually and precisely on the number line.