Linear Inequations-7

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Solve -5 ≤ (2 – 3x)/4 ≤ 9

Solution: We have,

-5 ≤ (2 – 3x)/4 ≤ 9

=>-5 X 4 ≤ (2 – 3x)/4 X 4 ≤ 9 X 4 [Multiplying throughout by 4]

=> -20 ≤ 2 – 3x ≤ 36

=> -20 – 2 ≤ 2 – 3x – 2 ≤ 36 – 2 [Subtracting 2 throughout]

=> -22 ≤ -3x ≤ 34

=> -22/-3 ≥ -3x/-3 ≥ 34/-3 [Dividing throughlut by -3]

=> 22/3 ≥ x ≥ -34/3

=> -34/3 ≤ x ≤ 22/3

=> x ∈ [-34/3, 22/3]

Hence, the solution set of the given system of inequations is the interval [-34/3, 22/3].

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