Question

$\frac{1}{2} (x + 1) + \frac{1}{3} (x - 1) = \frac{5}{12} (x - 2)$
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Answer 1

Answer:

$\frac{1}{2} (x + 1) + \frac{1}{3} (x - 1) = \frac{5}{12} (x - 2) \\ \\ = \frac{x + 1}{2} + \frac{x - 1}{3} = \frac{5x - 10}{12} \\ \\ = \frac{3x + 3 + 2x - 2}{6} = \frac{5x - 10}{12} \\ \\ = \frac{5x + 1}{6} = \frac{5x - 10}{12} \\ \\ = 6(5x - 10) = 12(5x + 1) \\ \\ = 30x - 60 = 60x + 12 \\ \\ = - 60 - 12 = 60x - 30x \\ \\ = - 72 = 30x \\ \\ = x = \frac{ - 72}{30} \\ \\ = x = \frac{ - 24}{10} \\ \\ = x = \frac{ - 12}{5}$

Answer 2

Question:

$\frac{1}{2} (x + 1) + \frac{1}{3} (x - 1) = \frac{5}{12} (x - 2)$

Solutions:

$\begin{gathered} \frac{1}{2} (x + 1) + \frac{1}{3} (x - 1) = \frac{5}{12} (x - 2) \\ \\ = \frac{x + 1}{2} + \frac{x - 1}{3} = \frac{5x - 10}{12} \\ \\ = \frac{3x + 3 + 2x - 2}{6} = \frac{5x - 10}{12} \\ \\ = \frac{5x + 1}{6} = \frac{5x - 10}{12} \\ \\ = 6(5x - 10) = 12(5x + 1) \\ \\ = 30x - 60 = 60x + 12 \\ \\ = - 60 - 12 = 60x - 30x \\ \\ = - 72 = 30x \\ \\ = x = \frac{ - 72}{30} \\ \\ = x = \frac{ - 24}{10} \\ \\ = x = \frac{ - 12}{5} \end{gathered}$