# Linear Inequalities

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