# Higher Algebra Hall & Knight Limiting Values & Vanishing Fractions (Chapter 20) Solutions

Hall and Knight Higher Algebra for Chapter 19 ‘Inequalities’ discuss the inequalities between the numbers. With the help of these solutions, you can easily prepare for engineering entrance exams such as IIT JEE. Inequality is a concept that you have been studying since Classes 10, 11 and 12. These solutions for Chapter 19 of Hall and Knight Higher Algebra will help you revise the basics of positive and negative quantities along with inequalities and linear inequalities.

Higher Algebra by Hall & Knight Chapter 19 Inequalities contains 2 exercises. There are a total of 42 questions in both the exercises that are determined from the concepts of the chapter. Go through all the questions and try to solve them with full dedication as the questions are designed according to the latest competitive exam patterns for JEE and NEET. In case you face any hurdle while solving the questions in the exercise you can access Instasolv for the solutions.

Our team of subject matter experts helps to provide you with accurate and online solutions to all the questions in Elementary Algebra and Higher Algebra by Hall & Knight. You can easily grasp how each solution has been done because of the step by step elaborations that we provide. The main aim is to provide you with the study material that will help you gain confidence and more knowledge.

## Important Topics for Hall and Knight Higher Algebra Solutions Chapter 19: Inequalities

**Positive or Negative Quantities**

In the chapter, we shall suppose that the letters always denote real and positive quantities. For example, any quantity ‘a’ is said to be greater than another quantity ‘b’ when ‘a-b’ is positive.

Thus, any positive number is greater than -1. Also, -5 is less than -2 because -5-(-2) is -3, that is negative. Based on this definition, n we can say that zero is greater than any negative quantity.

**Inequalities and Linear Equations **

The chapter inequalities concentrate on solving equations. This concept is all about solving inequalities by studying the basics of the concept.

We know that a<b which to an extension can also be written as a ≥ b. This term demonstrates that either a is greater than b or equal to the value of b.

Now you will study how to deal with the two inequalities that are >(greater than) or ≤ (less than or equal to).

You might also get to solve double inequalities so while solving them ensure to focus on the inequalities that are in the original problem. Here is an example of these types of questions from the chapter: If -1<x<4, then determine a and b in a<2x+3<b.

### Exercise Discussion in Hall and Knight Higher Algebra Solutions Chapter 19: Inequalities

- There are 2 exercises and 42 questions in Higher Algebra By H.S. Hall and S.R. Knight Chapter 19 Inequalities.
- In the first exercise, there are 23 questions that are formed from the concepts you study in the chapter. When you will solve these questions given in the exercise you will face questions like (b+c) (c+a) (a+b) > 8abc, show that the sum of any real positive quantity and its reciprocal is never less than 2, or questions like finding the maximum value of the given equation, and so on.
- The second exercise comprises 19 questions in all. These questions cover the concepts that are not covered in the previous exercise. The questions are like show that both the given expressions in the question are positive, or if x is positive then show that log(1+x)<x and > x/1+x and any other questions.
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