Inequalities-Introduction

CAT Exam
Until and unless you are a quant jock, you hate inequalities. It can also be said about absolute value. It is not very difficult. CAT is not about solving complicated equations/inequalities. It is about using your bare fundamentals, quietly, inconspicuously.CAT is not about booms and bangs and fancy equations; it is more ethereal; you have to be more in touch with your concepts. Let us start by saying that inequality just implies less than or greater than. Don’t try to read too much into it. Absolute value stands for the distance of a point from 0 on the number line. When |x| = 5, it means x is a point at a distance 5 from 0 on the number line. Take a minute to go through it again: x is a point at a distance 5 from 0 on the number line. Which points are at a distance 5 from 0 on the number line? Points 5 and -5. So x can take two values: 5 or -5. Similarly, if |x|  = 8, x can take two values x = 8 or x = -8. Now, what if you have something like |x-3| = 5? What does this mean? The distance you are looking for is still 5. The only difference is that the distance is from the point 3 now. Let’s look at the figure to see what values x can take. In the last example above, we say that twice the distance from 1.5 is 5. So we want the point that is 2.5 away from 1.5. If this makes sense to you, we could include an inequality sign here. Things will still be no different. For example, what values can x take if |x-3| < 5. We need those points where distance from point 3 is less than 5. At all the points depicted by the green line in the diagram below, the distance from 3 is less than 5. Point 4 is at a distance 1 away from 3, point 7 is at a distance 4 away from 3, 0 is at a distance 3 away from 3 and so on… Point 8 is at a distance 5 away from 3 so all points lying between 3 and 8 are at a distance less than 5 from 3. Point 3 is at a distance 0 from 3 so it is also included but 8 is not since the inequality doesn’t have an equal to sign. This is an extremely efficient way of working with inequalities + absolute value.

Category :

CAT Exam

Share This :

Join us MBA CET 2025