(3x + 5) / (4x + 2) = (3x + 4) / (4x + 7). Solve this linear equation.

(3x + 5) /  (4x + 2) = (3x + 4) / (4x + 7) 

(3x + 5) / (4x + 2) – (3x + 4) / (4x + 7) = 0 

((3x + 5) (4x + 7) – (3x + 4) (4x + 2)) / (4x + 2) (4x + 7) = 0 

By cross-multiplying we get, 

(3x + 5) (4x + 7) – (3x + 4) (4x + 2) = 0 

(3x + 5) (4x + 7) – (3x + 4) (4x + 2) = 0 

12x2 + 21x + 20x + 35 – 12x2 – 6x – 16x – 8 = 0 

19x + 35 – 8 = 0 

19x = – 27 

x = – 27 / 19 

On verifying the given equation, 

(3x + 5) / (4x + 2) = (3x + 4) / (4x + 7) 

By substituting the value of ‘x’, 

(3 (- 27 / 19) + 5) / (4 (- 27 / 19) + 2) = (3 (- 27 / 19) + 4) / (4 (- 27 / 19) + 7) 

(- 81 / 19 + 5) / (- 108 / 19 + 2) = (- 81 / 19 + 4) / (- 108 / 19 + 7) 

((- 81 + 95) / 19) / ((- 108 + 38) / 19) = ((- 81+76) / 19) / ((- 108 + 133) / 19) 

14 / 19 / – 70 / 19 = – 5 / 19 / 25 / 19 

– 14 / 70 = – 5 / 25 

– 1 / 5 = – 1 / 5

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