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Solve the following linear equations (3t - 2)/4 – (2t + 3)/3 = 2/3 – t

Solve the following linear equations
(3t - 2)/4 – (2t + 3)/3 = 2/3 – t 

Grade:12th pass

2 Answers

Harshit Singh
askIITians Faculty 5964 Points
2 months ago
Dear Student

(3t - 2)/4 – (2t + 3)/3 = 2/3 – t
⇒((3t–2)/4) × 12–((2t + 3)/3) × 12
⇒(3t - 2) × 3–(2t + 3) × 4 = 2 × 4–12t
⇒9t–6–8t–12=8–12t
⇒9t–6–8t–12=8–12t
⇒t–18=8–12t
⇒t + 12t = 8 + 18
⇒13t = 26
⇒t =2

Thanks
Shraddha Singh
273 Points
2 months ago
Dear Student,
 
(3t-2)/4 - (2t+3)/3 = 2/3 - t
Taking 12 as LCM,
[3×(3t-2) - 4×(2t+3)] / 12 = 2/3 - t
[9t-6 - 8t-12] / 12 = 2/3 - t
(t-18)/12 = (2-3t)/3
By cross multiplication,
3(t-18)= 12(2-3t)
3t-54 = 24-36t
39t = 78
t = 2
 
Hope it helps!
Thank you ✌️
 
 

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