To illustrate the differences between these inequalities on a graph, we can use a number line or a coordinate plane.
1. **Less Than (<)**: To graph the inequality x < a, you would draw an open circle on the point a and shade everything to the left. The open circle indicates that a is not included in the solution set.
2. **Greater Than (>)**: Similarly, for x > a, you place an open circle on a and shade to the right. Again, the open circle shows that a is not part of the solution.
3. **Less Than or Equal To (≤)**: When graphing x ≤ a, you use a closed circle on a to indicate that this value is included in the solution, and shade to the left.
4. **Greater Than or Equal To (≥)**: For the inequality x ≥ a, you would place a closed circle on a and shade to the right, indicating that a is part of the solution set.
In summary, the key difference lies in whether you use open or closed circles to represent whether the boundary value is included in the solution set. Shading shows the direction of the values that satisfy the inequality.