Tips & Tricks: Inequalities

# Tips & Tricks: Inequalities - Tips & Tricks for Government Exams - Bank Exams

## Introduction

In such types of questions of Inequality, a group of elements is given with a certain coded relationship denoted by <, >, =, ≤, ≥ and ≠.

To understand the symbols, let us discuss the meaning of the given symbols:

• ‘X > Y’; Here, the symbol ‘>‘ means ‘greater than’, hence the relation shows that X is greater than Z.
• ‘X < Y’; Here, the symbol ‘<‘ means ‘smaller than’, hence the relation shows that X is smaller than Z;
• ‘X = Y’; Here, the symbol ‘=’ means ‘equal to’, hence the relation shows that X is equal to Z;
• ‘X ≤ Y’; Here, the symbol ‘≤’ means ‘either smaller than or equal’, hence the relation shows that X is smaller than or equal to Z;
• ‘X ≥ Y’; Here, the symbol ‘≥’ means ‘either greater than or equal’, hence the relation shows that X is greater than or equal to Z;
• ‘X ≠ Y’; Here, the symbol ‘≠’ means ‘not equal’, hence the relation shows that X is not equal to Y. ### Tips

• If in a question, K < M < L is given, then K < M, M < L and K < L are considered to be true.
• If in a question, K > M ≥ L is given, then K > L is considered to be true and K ≥ L is not true.
• If in a question, K ≥ L = M is given, in that case, either K > M or K = M is true.
• If in a question, K < M > L is given, then no relation can be found between K and L because of opposite symbols.

### Types

1. Single statement Inequality:

• In this type of question, the relation between the elements is given in a single series by coded relationship symbols i.e. <, >, =, ≤, ≥ and ≠.

2. Multiple statements Inequality:

• In this type of question, the relation between the elements is given in two or more different series. To get the exact relation, we have to arrange it by matching the similar elements in a single series.

3. Not equal types Inequality:

• In this type of question, the ‘≠’ (not equal) relation are given between the elements. The not equal symbol is meant to show a comparison between the two quantities which are unequal hence, among the two quantities one will be either greater or smaller than the other quantity. To get the exact relation, we have to consider the both possibilities i.e. either ‘>’ or ‘<‘.

4. Filler Inequality:

• In this type of question, the relation between the elements is not given and in the place of coded symbols (which represented by <, >, =, ≤, ≥ and ≠) blank or space was/were given. You have to find out the proper coded symbol/s to fill the blank or space according to a certain conditions which generally mentioned with the questions.

5. Conditional Inequality:

• It is an inequality which is true for some variables or for a particular condition but not true for all values of variables.  And the solution of inequality consists of only real numbers as the term ” Less than or Greater than” are not defined for establish a certain relation.

### Solved Examples

Question for Tips & Tricks: Inequalities
Try yourself:Statements:

O=R, P=N>I, M≥R, N >M

Conclusions:

I.O<I

II.R<N

III.N<I

IV.O=I

Question for Tips & Tricks: Inequalities
Try yourself:Statements:

P<A>S, B=Q>T, S≤M<T

Conclusions:

I.P<T

II.S≤T

III.M<Q

IV.B=M

Question for Tips & Tricks: Inequalities
Try yourself:Statements:

G ≤ J < I, N ≥ K = H, N = F > G

Conclusions:

I.H<G

II.G<I

III.K=G

IV.K<G

Question for Tips & Tricks: Inequalities
Try yourself:Which of the following symbols should be placed in the blank spaces respectively *(in the same order, from left to right) in order to complete the given expression in such a manner that makes the expression ‘K > N’ and ‘M > O’ definitely false?

K__L__M__N__O

The document Tips & Tricks: Inequalities | Tips & Tricks for Government Exams - Bank Exams is a part of the Bank Exams Course Tips & Tricks for Government Exams.
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## Tips & Tricks for Government Exams

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## FAQs on Tips & Tricks: Inequalities - Tips & Tricks for Government Exams - Bank Exams

 1. What are inequalities in mathematics? Ans. Inequalities in mathematics are statements that compare two quantities and express the relationship between them using symbols such as greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤). These symbols indicate whether one quantity is larger or smaller than the other.
 2. How can I solve an inequality? Ans. To solve an inequality, follow these steps: 1. Treat the inequality sign as an equal sign and solve the equation. 2. Determine the critical values, where the inequality may change direction. 3. Plot these critical values on a number line. 4. Test a value from each region on the number line to determine if it satisfies the inequality. 5. Express the solution as an interval or a combination of intervals.
 3. What is the difference between solving equations and solving inequalities? Ans. Equations and inequalities both involve finding the values of variables, but they differ in terms of their solutions. Equations have a single solution, whereas inequalities often have a range of possible solutions. Inequalities also use different symbols to represent relationships between quantities, whereas equations typically use an equal sign (=).
 4. How can I graph an inequality on a coordinate plane? Ans. To graph an inequality on a coordinate plane, follow these steps: 1. Rewrite the inequality in slope-intercept form (y = mx + b). 2. Plot the y-intercept (b). 3. Use the slope (m) to find additional points on the line. 4. Draw a dashed or solid line through the points, depending on the inequality symbol. 5. Shade the region above or below the line, depending on the inequality symbol, to represent the solution set.
 5. Can you provide an example of solving an inequality? Ans. Sure! Let's solve the inequality: 2x + 5 > 9. First, subtract 5 from both sides to isolate the variable: 2x > 4 Next, divide both sides by 2 to solve for x: x > 2 The solution to the inequality is x > 2, which means that any value of x greater than 2 will satisfy the inequality.

## Tips & Tricks for Government Exams

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