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Ex 6.1, 16 - Solve: (2x - 1)/3 >= (3x - 2)/4 - (2 - x)/5 - Solving inequality  (one side)

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  1. Chapter 6 Class 11 Linear Inequalities
  2. Serial order wise
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Ex 6.1, 16 Solve the given inequality for real x: ((2๐‘ฅ โˆ’ 1))/3 โ‰ฅ ((3๐‘ฅ โˆ’ 2))/4โˆ’((2 โˆ’ ๐‘ฅ))/5 ((2๐‘ฅ โˆ’ 1))/3 โ‰ฅ ((3๐‘ฅ โˆ’ 2))/4 โˆ’((2 โˆ’ ๐‘ฅ))/5 ((2๐‘ฅ โˆ’ 1))/3 โ‰ฅ (5(3๐‘ฅ โˆ’ 2) โˆ’ 4(2 โˆ’ ๐‘ฅ))/(4(5)) ((2๐‘ฅ โˆ’ 1))/3 โ‰ฅ (15๐‘ฅ โˆ’ 10 โˆ’ 8 + 4๐‘ฅ)/20 ((2๐‘ฅ โˆ’ 1))/3 โ‰ฅ (15๐‘ฅ + 4๐‘ฅ โˆ’ 10 โˆ’ 8 )/20 ((2๐‘ฅ โˆ’ 1))/3 โ‰ฅ (19๐‘ฅ โˆ’ 18 )/20 20 (2x โ€“ 1) โ‰ฅ 3 (19x โ€“ 18) 40x โ€“ 20 โ‰ฅ 57x โ€“ 54 40x โ€“ 57x โ‰ฅ โ€“ 54 + 20 โ€“17x โ‰ฅ โ€“ 34 โ€“x โ‰ฅ (โˆ’34)/( 17) โ€“x โ‰ฅ โˆ’2 Since x is negative, we multiply both sides by -1 & change the signs (โ€“ 1) ร— (โ€“x) โ‰ค (โ€“1) ร— (โ€“2) x โ‰ค 2 Hence, x is a real number which is less than or equal to 2 Hence, x โˆˆ (โ€“โˆž, 2] is the solution

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