Linear Inequations

Solve the following linear inequations:
(i) 2x – 4 ≤ 0
(ii) -3x + 12 < 0
(iii) 4x – 12 ≥ 0
(iv) 7x + 9 > 30

Solution: (i) We have, 2x - 4 ≤ 0

=> (2x – 4) + 4 ≤ + 4 [Adding 4 on both sides]

=> 2x ≤ 4

=> 2x/2 ≤ 4/2

=> x ≤ 2

Hence, any real number less than or equal to 2 is a solution of the given inequation.

The solution set of the given inequation is (-∞, 2]

(ii) We have, -3x + 12 < 0

=>-3x < -12 [Transposing 12 on right side]

=> -3x/3 > -12/-3 [dividing both sides by -3]

=> x > 4

Thus, any real number greater than 4 is a solution of the given inequation.

Hence, the solution set of the given inequation is (4, ∞)

(iii) We have, 4x – 12 ≥ 0

=>4x ≥ 12 [Transposing 12 on RHS]

=> 4x/4 ≥ 12/4 [Dividing both sides by 4]

=> x ≥ 3

=> x ∈ [3, ∞)

Hence, the solution set of the given inequaiton is [3, ∞)

(iv) We have, 7x + 9 > 30

=>7x > 30 – 9 [Transposing 9 on RHS]

=> 7x > 21

=> 7x/7 > 21/7

=> x > 3

=> x ∈ (3, ∞)

Hence, the solution set of the given equation is (3, ∞).