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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