Inequalities such as greater than or less than involves in linear function is call linear inequalities. 

This lesson explains the linear inequalities of the forms \(x<a, x\le a,\)  and its graphs.

 

1. Inequalities of the form \(x < a \)

    For theThe inequalities of the form \(x < a \), the variable x takes all the values less than the 'a'.
    Since x is strictly less than a it does not take          the value ‘a’.  
    For example , x < 4 = { 3, 2, 1, 0 , -1, -2, -3 . . . . } for all integral values of x.

    Use the interactive graph given below to learn the graph of \(x < a \)    

2. Inequalities of the form \(x > a \)

    For theThe inequalities of the form \(x > a \), the variable x takes all the values less than the ‘a’.
    Since x is strictly less than a it does not take the value ‘a’.  
    For example , x > 4 = { 5, 6, 7, 8, . . . . } for all integral values of x.

notice

3. Inequalities of the form \(y < b \)

    For theThe inequalities of the form \(x < a \), the variable x takes all the values less than the 'a'.
    Since x is strictly less than a it does not take          the value ‘a’.  
    For example , x < 4 = { 3, 2, 1, 0 , -1, -2, -3 . . . . } for all integral values of x.

    Use the interactive graph given below to learn the graph of \(x < a \)    

Notice that the graph of y <=b has to be done with the solid line.

4. Inequalities of the form \(y > b \)

    For theThe inequalities of the form \(x < a \), the variable x takes all the values less than the 'a'.
    Since x is strictly less than a it does not take          the value ‘a’.  
    For example , x < 4 = { 3, 2, 1, 0 , -1, -2, -3 . . . . } for all integral values of x.

    Use the interactive graph given below to learn the graph of \(x < a \)    

Notice that the graph of y >= b is to be made with the solid line at y=b

 

Notice that