Inequalities

So far we have seen equations in which both sides are equal. Now let us find out about the inequalities.
Look at the balance scales given below.

First balance scale has no weights in it and it is perfectly balanced whereas the second balance scale has more weight on left side and it is not balanced.

Equations also work in the same way as the balance works. If the left hand side of the equation is less than right hand side we use the < (less than) sign to represent it. Simillarly if the left hand side is more than right hand side we use >(greater than) sign.

We know that the graph for Y = 5 will be a straight line on which at every point the y-coordinate's value is equal to 5 .
Similarly the graph for Y < 5 will cover all the area in which the y-coordinate's value is less than 5.

In the above graph, all the dotted area represents Y < 5.
Can you guess how will the graph for the equation x 3 will look?


Few simple facts that you should know



Do you know that all the methods and hints we use to solve equalities are also applicable to inequalities?
Example:
If we add or take out the same weight to or from both the sides of the unbalanced balance scale it will not make any difference to the balance.
2X > 5 is equivalent to 2X + 3 > 5 + 3
An inequality does not change when we add or subtract the same term to both sides.
Example:
4X 5 is equivalent to 4X / 3 5 / 3
An inequality does not change when we multiply or divide both sides by the same term.
Example:
X < 10 is equivalent to X 2 < 10 2
An inequality does not change when we raise both sides to the same exponent.