Solutions of Inequalities

Any solution to an inequality is the value of that variable which makes inequality a true statement. For example, suppose we have an inequality x < 5. In such a case, all the values of x which are less than 5 make this inequality a true inequality. While solving inequalities we need to keep some rules in mind, 

1. Equal numbers can be added or subtracted from both sides of the inequality.
2. Both sides of an inequality can be multiplied (or divided) by the same positive number. But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed.

These operations do not affect the inequality and can be used to simplify the inequality for us. 

Question: Solve the inequality 20x < 80 and show its solutions on a graph. 

Solution: 

We are given, 

20x < 80

We know dividing the inequality by a positive number doesn’t change anything. Let’s divide the inequality with 20. 

x < 4. 

Now all the value less than 10 are solutions to this inequality. The figure below represents this solution on graph. 

We know how to formulate equations of different degree, and it is used a lot in real life, but the question arises, is it always possible to convert a situation into an equation? Sometimes we get statements like, the number of Covid cases per day in Delhi has reached more than 10,000. This phrase “Less than”, “Greater than”, “less than or equal to” etc. Such phrases are difficult to translate into equations. For such cases, we need to learn how to make equations with inequalities in them. Let’s see this in detail.