Linear Inequality

Related Words

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

    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 ?

    example of  Linear Inequality
    Choices:
    A. Graph 1
    B. Graph 2
    C. Graph 3
    D. Graph 4
    Correct Answer: A

Solution:

    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>
      example of  Linear Inequality
    Step 2: Test a point, which is not on the boundary line.
    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).
      example of  Linear Inequality
    Step 4: Therefore, Graph 1 best suit the inequality y < x -4

Translate :