Question

2x-1/3=2/3x+4 find the value of x

Answer 1

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$\large\mathcal\red{solution}$

$2x - \frac{1}{3} + \frac{2}{3x} = 4 \\ = > 2x + \frac{2}{3x} = 4 + \frac{1}{3} \\ = >3 \times ( 6x {}^{2} + 2) = 13 \times 3x \\ = > 6x {}^{2} + 2 = 13x \\ = > 6x {}^{2} - 13x + 2 = 0 \\ = > 6x {}^{2} - 12x - x + 2 = 0 \\ = > 6x(x - 2) - (x - 2) = 0 \\ = > (6x - 1)(x - 2) = 0 \\ so \: either \: (6x - 1) = 0 = > x = \frac{1}{6} \\ or \: \: (x - 2) = 0 = > x = 2$