Linear Inequations ICSE Class 10 Maths Quiz MCQ

linear-inequations-icse-class-10-maths-quiz-mcq

You are familiar with the term linear equation. You have also learned how to solve a linear equation. Now let us understand a new concept Inequations, also known as inequalities. In this online maths quiz, you will find 10 such multiple-choice questions based on the above concept. So, before attempting this maths online quiz on Linear inequations let us understand what are linear inequations and how it is solved.

Linear inequations 


Statements such as x > 5, y < 3, 3x - 8  7, 2x + 5 ≥ 3
are called linear inequations in one variable. These sentences say that one thing is not equal to another. 
In general, a linear inequation in one variable can be written as ax + b < 0, ax + b > 0, ax + b ≤ 0, ax + b ≥ 0, 
where a and b are real numbers and a ≠ 0.

Consider these two statements:
(a) 5x = 10 (b) 2x < 5

If the variable x in the equation (a) is replaced by 2, it provides a true statement. We say that the equation is satisfied.
Similarily, equation (b) is satisfied if the variable x is replaced by the numbers ... , -2, -1, 0, 1, 2 

Replacement set:

The set from which values of the variable in the inequation are chosen is called replacement set.

Solution set:

The set of all the solutions of an inequation is called the solution set of the inequation. It is a subset of the replacement set.

 Replacement Set
 Solution Set
 (i)  { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
 { 1, 2, 3 }
 (ii) { 5, 6, 7, 8, 9, 10 }
 
 (iii) { -5, 10 }
 { -5 }

The above examples illustrate the fact that the solution of an inequation depends upon the replacement set used. It also follows from the above examples that an inequation may have one, many, or no solution depending upon the replacement set. In this online maths quiz on the chapter Linear inequations for ICSE class 10 students, you will get multiple-choice questions on a replacement set too.

Notation


The following notations should be known before attempting the sums on linear inequations:

N = Set of all natural numbers
W = Set of all whole numbers
Z/I = Set of all integers
R = Set of all real numbers

Properties of Inequations


1. Adding to or subtracting from both sides of an inequation any non-zero number produces an equivalent inequation.

(i) x - 5 < 7 is equivalent to x - 5 + 5 < 7 + 5 or x < 12
(ii) x + 5 < 7 is equivalent to x + 5 - 5 < 7 - 5 or x < 2

2. Multiplying or dividing both sides of an inequation by the same positive number produces an equivalent inequation.

(i) 2x > 16 is equivalent to 2x/2 > 16/2 or x > 8
(ii) x/2 >16 is equivalent to (x/2)*2 > 16 * 2 or x > 32

3. Multiplying both sides of an inequality by the same negative number produces an inequality with its direction reversed.

(i) x < 5 is equivalent to (-1) (x) > (-1) (5) or -x > -5
(ii) -x < -5 is equivalent to (-1) (-x) > (-1) (-5) or x > 5

4. Dividing each side of an inequation with a positive number does not change the inequation.

(i) 2x > 12 ⇒ 2x/2 > 12/2 ⇒ x > 6

5. Dividing each side of an inequation by a negative number reverses the inequation.

(i) -2x > 12 ⇒ -2x/-2 < 12/-2 ⇒ x < -6


Online Maths Quiz Linear Inequations ICSE Class 10 MCQ



Below are the quiz and the rules to be followed while performing this online test quiz. 
You can go through the tutorial of this chapter in video form to understand the concept clearly. Here is the link to the video tutorial.

Video tutorial on Linear inequations ICSE Class - X


Rules For The Quiz:


  • This quiz has 10 multiple-choice questions.
  • Each sum has 2 marks.
  • So the maximum marks are 20.
  • There is no time limit.
  • You should be ready with a pen and copy in your hand to solve the sums.
  • keep your Maths book away from you. This is the test of your memory. So do not take the help of the Maths book.
  • The correct answer and explanation are provided at the end of this quiz.

 
Do share your score of this quiz in the comments section below.
Happy learning. Say yes to maths.

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