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