Linear Inequations-1

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Solve the following inequations:
(i)3x + 17 ≤ 2(1 - x)
(ii) 2(2x + 3) – 10 ≤ 6(x - 2)

Solution: (i) We have, 3x + 17 ≤ 2(1 - x)

=>3x + 17 ≤ 2 – 2x

=> 3x + 2x ≤ 2 – 17 [Transposing -2x to LHS and 17 to RHS]

=>5x ≤ -15

=> 5x/5 ≤ -15/5

=> x ≤ -3

=> x ∈ (-∞ -3]

Hence, the solution set of the given inequation is (-∞ -3].

(ii) We have, 2(2x + 3) – 10 ≤ 6(x - 2)

=>4x + 6 – 10 ≤ 6x – 12

=> 4x – 4 ≤ 6x – 12

=> 4x – 6x ≤ -12 + 4 [Transposing -4 to RHS and 6x to LHS]

=> -2x ≤ -8

=> -2x/-2 ≥ -8/-2

=> x ≥ 4

=> x ∈ [4, ∞)

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

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