to the study of linear inequalities in one and two variables only. MATHEMATICS . Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation Let us consider the inequality ( ) of Section . , viz, x < Note that here x denotes the number of packets of rice.
Obviously, x cannot be a negative integer or a fraction. Left hand side (L.H.S.) of this inequality is x and right hand side (RHS) is . Therefore, we have For x = , L.H.S. = ( ) = < (R.H.S.), which is true.
For x = , L.H.S. = ( ) = < (R.H.S.), which is true. For x = , L.H.S. = ( ) = < , which is true.
For x = , L.H.S. = ( ) = < , which is true. For x = , L.H.S. = ( ) = < , which is true.
For x = , L.H.S. = ( ) = < , which is true. For x = , L.H.S. = ( ) = < , which is true.
For x = , L.H.S. = ( ) = < , which is false. In the above situation, we find that the values of x , which makes the above inequality a true statement, are , , , , , , . These values of x , which make above inequality a true statement, are called solutions of inequality and the set { , , , , , , } is called its solution set .
Thus, any solution of an inequality in one variable is a value of the variable which makes it a true statement. We have found the solutions of the above inequality by trial and error method which is not very efficient. Obviously, this method is time consuming and sometimes not feasible. We must have some better or systematic techniques for solving inequalities.
Before that we should go through some more properties of numerical inequalities and follow them as rules while solving the inequalities. You will recall that while solving linear equations, we followed the following rules: Rule