Solution Set (Linear Inequality)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The solution set for linear inequalities in the coordinate plane is the collection of all points (x, y) that satisfy the inequality. This set represents all the ordered pairs that make the inequality true.
When graphed, the solution set is typically represented as a region in the plane, determined by:
Boundary Line: The line that corresponds to the related linear equation (obtained by replacing the inequality sign with an equals sign).
Shading: The area above or below the boundary line (or on one side of it), depending on whether the inequality is strict (< or >) or inclusive (< or >). This shading indicates all the points that satisfy the inequality.
For example:
For the inequality y < 2x + 3, the boundary line is y = 2x + 3 (dashed), and the shading is below this line, representing all the points where y is less than 2x + 3.
In summary, the solution set encompasses all points within the shaded region that fulfill the conditions of the inequality, providing a complete description of all possible solutions in the coordinate plane.