Linear Inequality

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
    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="">
      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="">
    0 < 0=""><>
    0 < -="">
    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="">

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