# CAT Online Live Classes

Algebra - Inequalities

### Concepts discussed on March 17, 2018

#### Algebra - Inequalities

Welcome to the live session of Inequalities. The concepts and questions discussed on March 17, 2018 during the live session follow the embedded video. The video link next to each concept will take you to the start of the part of the video where that specific concept is discussed. Click the video embedded below to watch the entire session.

#### Easy Questions

1. Find the range of x that satisfies the equation $|2x + 5| < |3x – 6|$.

2. #### Medium Questions

3. What is the range of values of x that satisfy x (x-2) (x+4) > 0

4. Find the range of x that satisfies the equation $\frac{(|x| − 1)}{(|x| − 3)} < 0.$

5. Find the range of x that satisfies the equation $x^2 – 5|x| + 6 > 0$.

6. Find the range of x that satisfies the equation $||2x – 4|+ 3| < 7$.

7. x + 2y + 3z = 50. x, y, z are natural numbers. What is the maximum value of $x^2 + y^2 + z^2 ?$.

8. x + 3y = 32. x, y are natural numbers. What is the maximum value of xy?

9. #### Tough Questions

10. If x belongs to the range (-5, 5), what is the probability that | [x] + 1| > [|x| + 1], where [x] represents the greatest integer less than or equal to x?