Solve the given inequality for real x: [3x/5 + 4]/2 ≥ (x-6)/3
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Given : (3x/5 + 4)/2 ≥ (x-6)/3
To find : Solve for x
Solution:
(3x/5 + 4)/2 ≥ (x-6)/3
multiplying by 6 on both sides
=> 3(3x/5 + 4) ≥ 2(x-6)
=> 9x/5 + 12 ≥ 2x - 12
adding 12 - 9x/5 both sides
=> 24 ≥ 2x - 9x/5
=> 24 ≥ (10x - 9x)/5
=> 24 ≥ x/5
multiplying by 5 both sides
=> 120 ≥ x
=> x ≤ 120
=> x ∈ ( - ∞ , 120 ]
x ∈ ( - ∞ , 120 ]
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