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The problems related to inequality are asked in the quantitative aptitude section of the CAT examination. There are at the very least two problems asked related to this topic every year. Along with being a scoring topic, this is relatively easier compared to some of the other concepts. Also, this topic is related greatly to other topics, like the solution of equations, linear expressions, quadratic expressions, etc. This concept makes up the very basis of the plotting of the graphs and finding out the solutions to inequalities.
Concepts of Inequalities for CAT Exam
As you already knew, the inequality expression is a situation in which the terms of either side of the symbol of inequality are not equal to each other. Besides being unequal, it can be anything. The conditions that work under the principles of inequality are <, >, ≤, ≥, «, », ≠, etc. The expressions that consist of these symbols can be termed as expressions that have inequality in them.
Most of the time, the questions that are asked regarding inequality are about the plotting of a graph. So, for you to be able to plot a graph, you firstly need to be able to find the solutions to an equation. For that, you need to have an understanding of what inequality is and what the symbols used for the types of inequality signify.
You need to have an understanding of the properties that are related to the problems of inequality. These properties include the effects that a value will have on the expressions after it is added, subtracted, multiplied with, or divided by that certain value. The understanding of inequality gives a brief account of all those changes. Also, it carries a relatively higher significance in daily life too.
Tricks for solving inequalities related questions for CAT exams
The solution of inequalities mainly depends on the type of equation that it comprises.
When the equation is linear:
When the given expression has a linear equation on both sides of the inequality symbol, it will be best to split that expression into two equations. Find out the solutions of both the expressions separately but by putting the same values for the variables to check the effectiveness of the solutions. After getting the accurate measure of the solutions, you can plot the graph for the respective solutions quite easily.
When the equation is quadratic:
When the expression carries quadratic equations on both of its sides, it will be best suited to apply the principle of transposition to it. Ensure that one of the sides of the expression is a perfect zero. After that is done, find the solution to the new quadratic equation that is formed after the previous operation. Now, using the solutions that you received out of the quadratic equation, plot the graphs that are needed.
When you are trying to show inequality in an expression:
To arrive at completely accurate solutions, keep in mind the properties of inequalities. Alter your problems following the properties and get the desired result. Just keep in mind that the same value will be used on both sides with the same mathematical operation.
Solved examples of Inequalities questions for CAT Exams
Give the range of f(x) = x2 – 6x + 14.
The range of the given function can be given as follows:
(0, ∞).
This is because, for the upper limit and the lower limit of the interval, the function will give a positive result. And, the outcome will remain the same even if a number between the two limits is chosen.
Evaluate: −2 < (6 − 2x) / 3 < 4
Multiplying all the values by 3;
−6 < 6−2x < 12
Now, subtracting 6 from each value;
−12 < −2x < 6
Dividing all parts by 2;
−6 < −x < 3
This is the interval in which the value of ‘x’ lies.
Evaluate: 6x – 8 > x + 7
Transposing to put values of the same type on either side;
6x – x > 7 + 8
Simplifying;
5x > 15
x > 3
Conclusion
There is a certain set of properties that are followed by all types of inequalities. By utilising all of these properties to their full extent, we can find the solutions to all kinds of equations. As there is no equality in inequalities, we need to insert more data within the given equation. This data can be effectively provided with the help of the properties of inequalities. Therefore, to be able to solve equations to a higher level, an understanding of inequalities is a must.
