Question

(3x -4)/7 + 7/(3x -4) = 5/2, x≠ 4/3​

Answer 1

Answer:

x=2

Step-by-step explanation:

$\frac{(3x - 4)}{7} + \frac{7}{(3x - 4)} = \frac{5}{2} \\ \frac{(3x - 4) (3x - 4) + 7(7)}{7(3x - 4)} = \frac{5}{2} \\ \frac{3x(3x - 4) - 4(3x - 4) + 49}{7(3x) - 7(4)} = \frac{5}{2} \\ \frac{9x - 12x - 12x + 16 + 49}{21x - 28} = \frac{5}{2} \\ \frac{9x - 24x + 65}{21x - 28} = \frac{5}{2} \\ \frac{ - 15x + 65}{21x - 28} = \frac{5}{2} \\ cross \: multiplication \\ 2( - 15x + 65) = 5(21x - 28) \\ - 30x + 130 = 105x - 140 \\ 130 + 140 = 105x + 30x \\ 270 = 135x \\ \frac{270}{135} = x \\ 2 = x \\ therefore \: x = 2$