Here we will discuss about properties of inequation or inequalities.
1. The inequation remains unchanged if the same number is added to both sides of inequation.
For example:
(i) x  2 > 1
⇒ x  2 + 2 > 1 + 2 (by adding 2 to both sides)
⇒ x > 3
(ii) x < 5
⇒ x + 1 < 5 + 1 (by adding 1 to both sides)
⇒ x + 1 < 6
(iii) x  3 > 2
⇒ x  3 + 3 > 2 + 3 (by adding 3 to both sides)
⇒ x > 5
2. The inequation remains unchanged if the same number is subtracted from both sides
of the inequation.
For example:
(i) x + 3 ≤ 7
⇒ x + 3  3 ≤ 7  3 (by subtracting 3 from both sides)
⇒ x ≤ 4
(ii) x ≥ 4
⇒ x  3 ≥ 4  3 (by subtracting 3 from both sides)
⇒ x  3 ≥ 1
(iii) x + 5 ≤ 9
⇒ x + 5  5 ≤ 9  5 (by subtracting 5 from both sides)
⇒ x ≤ 4
3. The inequation remains unchanged if the same positive number is multiplied to both
sides of the inequation.
For example:
(i) x/3 < 4
⇒ x/3 × 3 < 4 × 3 (Multiplying 3 to both sides.)
⇒ x < 12
(ii) x/5 < 7
⇒ x/5 × 5 < 7 × 5 (Multiplying 5 to both sides.)
⇒ x < 35
4. The inequation changes if the same negative number is multiplied to both sides of the
inequation. It reverses.
For example:
(i) x/5 > 9
⇒ x/5 × (5) < 9 × (5)
⇒ x < 45
⇒ x > 45
(ii) x > 5
⇒ x × (1) < 5 × (1)
⇒ x < 5
(iii) x/(2) > 5
⇒ x/(2) × (2) < 5 × (2)
⇒ x < 10
5. The inequation remains unchanged if the same positive number divides both sides of the inequation.
For example:
(i) 2x > 8
⇒ 2x/2 > 8/2 (Dividing both sides by 2)
⇒ x > 4
(ii) 5x > 8
⇒ 5x/5 > 8/5 (Dividing both sides by 5)
⇒ x > 8/5
6. The inequation changes if the same negative number divides both sides. It reverses.
For example:
(i) 3x > 12
⇒ 3x/3 < 12/3 (Dividing both sides by 3)
⇒ x < 4
(ii) 5x ≤ 10
⇒ 5x/5 ≥ 10/5 (Dividing both sides by 5)
⇒ x ≥ 2
(iii) 4x > 20
⇒ (4x)/(4) < 20/(4) (Dividing both sides by 4)
⇒ x < 5
Write the inequality obtained for each of the following statements.
(i) On adding 9 to both sides of 21 > 10.
(ii) On multiplying each side of 4 < 12 by 3.
Solution:
(i) We know that adding the same number to both sides of inequality does not change the inequality.
21 + 9 > 10 + 9
⇒ 30 > 19
(ii) We know that multiplying each side of an equality by the same negative number reverses the inequality.
Therefore, 4 < 12, then 4 × 3 > 12 × 3
⇒ 12 > 36
● Inequations
Properties of Inequation or Inequalities
Representation of the Solution Set of an Inequation
Practice Test on Linear Inequation
● Inequations  Worksheets
Worksheet on Linear Inequations
7th Grade Math Problems
8th Grade Math Practice
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