Properties of Inequations
- Adding same number to each side of an inequation does not change the inequality
Example. (i) x + 2 < 5 ? x + 2 + 3 + < 5 + 3
(ii) 2x + 3 > + 8 ? 2x + 3 + 2 > 8 + 2
2. Subtracting same number from each side of an inequation does not change the inequality
Example. (i) 3x + 4 < 9 ? 3x + 4 – 2 < 9 – 2
(ii) 2x + 5 > 12 ? 2x + 5 – 5 > 12 – 5
3. Multiplying each side of an inequation by same positive number does not change the inequality
Example. (i) x/3 < ? x/6 × < 3 × 6 (ii) x/2 < 5 ? x/2 × 2 < 5 × 2
4. Multiplying each side of an inequation by the same negative number reverses the inequality
Example. (i) – x > 1 ? x < - 1 [Multiplying each side by – 1]
(ii) – x/2 < 3 ? x > 3 × (- 2) [Multiplying each side by – 2]
5. Dividing each side of an inequation by the same positive numberdoes not change the inequality
Example. (i) 2x < 6 ? x < 3 [Dividing each side by 2]
(ii) 3x > 9 ? x > 3 [Dividing each side b y 3]
Example
Example1. Solve:
(i) 3x – 4 < 5, x ? W (ii) x/3 + 4 > 6, x ? N
.Solution. We have
(i) 3x – 4 < 5 ? 3x < 9 [Adding 4 on each side]
? x < 3 [Dividing each side by 3]
... Solution set = {x ? W : x < 3} = {0, 1, 2}
(ii) x/3 + 4 > 6 ? x/3 < 2 [Subtracting 4 from each side]
? x > 6 [Multiplying each side by 3]
... Solution set = {x ? N : x < 6} = {7, 8, 9, 10, ……….}
Example2. Solve:
(i) 5 – 2x < 3, x ? N (ii) 7 – 4x > 12, x ? I
Solution. We have
(i) 5 – 2x < 3 ? - 2x < - 2 [Subtracting 5 from each sides]
? x > 1 [ Dividing each side by – 2]
... Solution set = {x ? N : x > 1} = {2, 3, 4, 5, 6, ……….}
(ii) 7 – 4x > 12 ? 4x < 5 [Subtracting 7 from each sides]
? x < - 5/4 [Dividing each side by – 4]
... Solution set = {x ? I : x < - 5/4} = { - 2, - 3, - 4, ………..}
Example3. Solve the inequation 2x – 1 < 9 , x ? W. y
Solution. We have
2x – 1 < 9 ? 2x < 10 [Adding 1 on each side]
? x < 5 [Dividing each side by 2]
... Solution set = {x ? W : x < 5} = {0, 1, 2, 3, 4}
Related Tags
Simple Equations, Simple Equations examples ,Simple Equations problems