Learn Inequalities For JEE Main

A linear inequality is a topic that has great importance when the JEE Main exam is concerned. Inequality is used to compare two numbers or expressions. JEE aspirants can easily score marks from this topic if they have a strong command over inequalities. Students can expect 1-2 questions from inequalities for the JEE exam and any competitive exam. So they are recommended to revise and practice this topic properly. 

An equation is different from an inequality. We can say that inequalities are expressions in which the RHS and LHS are not equal. We use the symbols, less than (<), greater than (>), greater than or equal to (≥), less than or equal to (≤), not equal to ≠. In this article, we will discuss what are inequalities in Math. An inequality is used to make a non-equal comparison between two numbers or other mathematical expressions. The two important inequalities are: 

• Linear inequality 
• Quadratic inequality

Strict Inequality

The symbol > denotes greater than. For eg. p>q means, p is greater than q. This means p is strictly greater than q. Here equivalence is not used. The symbol < denotes less than. For eg. p<q means, p is less than q. This means p is strictly less than q. Less than symbol and greater than symbol is considered as the strict inequality symbols. 

While explaining what are inequalities in Math, we should consider slack inequality also.

Slack Inequality

The symbols, less than or equal to (≤) and greater than or equal to (≥) are the slack inequality symbols. A relation between two inequalities that are not strict is denoted by the slack inequality. For example, p≤q implies p is less than or equal to q. p≥q implies p is greater than or equal to q. 

Let us have a look at some examples of solving inequalities.

Example 1: The solution set of the inequality 37 – (3x + 5) ≥ 9x – 8 (x – 3) is

Solution:

Given 37 – (3x + 5) ≥ 9x – 8 (x – 3)

=> 32 – 3x ≥ x + 24

=> 32 – 24 ≥ 3x + x

=> 8 ≥ 4x

=> x ≤ 2

Or x ∈ (-∞, 2]

Example 2: Find the solution of 2x – 1 = |x + 7| is

Solution:

Given 2x – 1 = |x + 7|

If x ≥ -7, 2x-1 = x+7

=> x = 8

If x≤ -7, 2x-1 = -(x+7)

=> x = -2, is not possible. 

So x = 8.

The solution is given by x = 8.

Quadratic Inequalities

Inequality having a quadratic expression is a quadratic inequality. Students can easily solve inequalities by following the rules. While solving quadratic inequalities, write the inequality as an equation. Then solve the equation. Mark the solutions on the number line and find the intervals. Then choose a random number from each interval and check whether the inequality is true for that number. The values which satisfy the inequality are the solutions.

Students are recommended to revise and practise previous years’ questions so that they can be familiar with the type of questions asked from inequalities. Stay tuned to BYJU’S for important formulas pdf on inequalities and previous years’ JEE solved question papers.