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Fundamental Theorem of Arithmetic

Solve: 3x +...

Question

Solve: $\frac{3 x + 2}{7} + \frac{4 (x + 1)}{5} = \frac{2}{3} (2 x + 1)$

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Solution

We have,

$\frac{3 x + 2}{7} + \frac{4 (x + 1)}{5} = \frac{2}{3} (2 x + 1)$

$\frac{5 (3 x + 2) + 28 (x + 1)}{5} = \frac{2}{3} (2 x + 1)$

$\frac{15 x + 10 + 28 x + 28}{5} = \frac{4 x + 2}{3}$

$\frac{43 x + 38}{5} = \frac{4 x + 2}{3}$

$129 x + 114 = 20 x + 10$

$109 x = - 104$

$x = - \frac{104}{109}$

Hence, the value of $x$ = $- \frac{104}{109}$ .

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3^{2 x + 1} = 3^{x + 2} + \sqrt{1 - {6.3}^{x} + 3^{2 (x + 1)}}

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