Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Last updated at May 29, 2023 by Teachoo

Ex 5.1, 16 Solve the given inequality for real x: ((2π₯ β 1))/3 β₯ ((3π₯ β 2))/4β((2 β π₯))/5 ((2π₯ β 1))/3 β₯ ((3π₯ β 2))/4 β((2 β π₯))/5 ((2π₯ β 1))/3 β₯ (5(3π₯ β 2) β 4(2 β π₯))/(4(5)) ((2π₯ β 1))/3 β₯ (15π₯ β 10 β 8 + 4π₯)/20 ((2π₯ β 1))/3 β₯ (15π₯ + 4π₯ β 10 β 8 )/20 ((2π₯ β 1))/3 β₯ (19π₯ β 18 )/20 20 (2x β 1) β₯ 3 (19x β 18) 40x β 20 β₯ 57x β 54 40x β 57x β₯ β 54 + 20 β17x β₯ β34 βx β₯ (β34)/( 17) βx β₯ β2 Since x is negative, we multiply both sides by β1 & change the signs (β 1) Γ (βx) β€ (β1) Γ (β2) x β€ 2 Hence, x is a real number which is less than or equal to 2 Hence, x β (ββ, 2] is the solution