Definition of Linear Inequality
A Linear Inequality involves a linear expression in two variables by using any of the relational symbols such as <,>, ≤ or ≥
More About Linear Inequality
- A linear inequality divides a plane into two parts.
- If the boundary line is solid, then the linear inequality must be either ≥ or ≤.
- If the boundary line is dotted, then the linear inequality must be either > or <.
Example of Linear Inequality
Video Examples: Solving Linear Inequalities
- As the boundary line in the above graph is a solid line, the inequality must be
either ≥ or ≤.
Since the region below the line is shaded, the inequality should be ≤.
We can notice that the line y = - 2x + 4 is included in the graph; therefore, the inequality is y = - 2x + 4. Any point in the shaded plane is a solution and even the points that fall on the line are also solutions to the inequality.
- 4x + 6y = 12, x + 6 ≥ 14, 2x - 6y < 12 + 2x, 9y < 12 + 2x are the examples of inear inequalities.>
Solved Example on Linear Inequality
Ques: Which of the graphs best suits the inequality y < x < -4 ?
Choices:A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4
Correct Answer: A
Step 1: Since the inequality 'involves less than' (<), use dashed boundary
line to graph the inequality y < x - 4 as in the
below shown graph>
Test (0, 0) in the inequality.
y < x - 4 [substitute.]
0 < 0 < -4
0 < - 4[False]
Step 3: Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).