Ex 5.1, 16 - Chapter 5 Class 11 Linear Inequalities
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 5.1, 16 Solve the given inequality for real x: ((2๐ฅ โ 1))/3 โฅ ((3๐ฅ โ 2))/4โ((2 โ ๐ฅ))/5 ((2๐ฅ โ 1))/3 โฅ ((3๐ฅ โ 2))/4 โ((2 โ ๐ฅ))/5 ((2๐ฅ โ 1))/3 โฅ (5(3๐ฅ โ 2) โ 4(2 โ ๐ฅ))/(4(5)) ((2๐ฅ โ 1))/3 โฅ (15๐ฅ โ 10 โ 8 + 4๐ฅ)/20 ((2๐ฅ โ 1))/3 โฅ (15๐ฅ + 4๐ฅ โ 10 โ 8 )/20 ((2๐ฅ โ 1))/3 โฅ (19๐ฅ โ 18 )/20 20 (2x โ 1) โฅ 3 (19x โ 18) 40x โ 20 โฅ 57x โ 54 40x โ 57x โฅ โ 54 + 20 โ17x โฅ โ34 โx โฅ (โ34)/( 17) โx โฅ โ2 Since x is negative, we multiply both sides by โ1 & change the signs (โ 1) ร (โx) โค (โ1) ร (โ2) x โค 2 Hence, x is a real number which is less than or equal to 2 Hence, x โ (โโ, 2] is the solution
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo