Revision Notes for ICSE Class 10 Math Chapter 4 - Free PDF Download
FAQs on ICSE Class 10 Mathematics Revision Notes Chapter 4 - Linear Inequations
1. From where should students study the revision notes of Chapter 4 Linear In equations In One Variable of the ICSE Class 10th Mathematics?
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2. What are the postulates of inequality?
The postulates of inequality are mentioned below:
- An equivalent inequality is produced when a non-zero number is added or subtracted from both sides of the inequality. For example, x + 5 > 8 is equivalent to x + 5 + 9 > 8 + 9 and x + 5 – 1 >8 – 1.
- When the same positive number is multiplied and divided on both sides of the inequality then inequality is produced. For example, 6x > 7 is equal to 6x * 3 >7 * 3 and 6x/ 3 > 7/ 3.
- If a negative number is multiplied on both sides of the inequality then the reversed inequality is produced. For example, x > 4 is equivalent to x * (-2) <4 * (-2).
3. Define the following terms:
(A) Universal set
(B) Replacement set
(C) Solution set
(A) Universal Set –The value of a variable is chosen from a set of numbers. This set is known as the universal set.
(B) Replacement Set –It is a kind of a universal set. From the replacement set, the values for a variable are chosen.
(C) Solution Set –The subset of the replacement set is called the solution set. The elements of this subset satisfy the given inequality.
For example, consider the set of natural numbers N. This set is the universal set or the replacement set, the solution set will be {1, 2, 3} for a given inequality.
4. Differentiate between the terms Inequalities and Inequations.
Inequalities –The signs which are used to compare two numbers or expressions are known as inequalities. These signs are greater than, less than, greater than or equal to, less than or equal to or not equal to signs.
Inequations –An equation or a mathematical statement in which the value of variables is not equal to the other value is known as inequation. These inequations are written with help of the inequalities.
For example, 4x + 5 > 9 is an inequation and the sign ‘>’ is an inequality.
5. Find the solution of the following inequalities:
(I) 4x – 1 >x + 11
(II) 2 – 3x > 7 – 5x
(III) 2x –5/ 3 > 3x – 3
(I) 4x – 1 >x + 11
3x > 12
x > 4
4 is the end range of the given inequality.
(II) 2 – 3x > x + 11
2x >5
x > 5/ 2
x >2.5
2.5 is the end range of the inequality.
(III) 2x – 5/ 3 >3x – 3
2x – 5 > 9x -9
-7x > (-14)
x <2
2 is the end range of the inequality.
In all the above in equations, less than and more than sign is used, therefore the end range 4, 2.5 and 2 is represented as the hollow circle on the number line. You can visit Vedantu for online learning resources and chapter-wise solutions for free.