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Solving Equations with Variable on Both Sides

2 x-13-6 x-25...

Question

$\frac{2 x - 1}{3} - \frac{6 x - 2}{5} = \frac{1}{3}$

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Solution

$\begin{array}{l} We have: \\ \frac{2 x - 1}{3} - \frac{6 x - 2}{5} = \frac{1}{3} \\ \Rightarrow \frac{5 (2 x - 1) - 3 (6 x - 2)}{15} = \frac{1}{3} \\ \Rightarrow \frac{10 x - 5 - 18 x + 6}{15} = \frac{1}{3} \\ \Rightarrow \frac{- 8 x + 1}{15} = \frac{1}{3} \\ \Rightarrow - 8 x + 1 = \frac{1}{3} \times 15 \\ \Rightarrow - 8 x = 5 - 1 \\ \Rightarrow - x = \frac{4}{8} \\ \Rightarrow x = - \frac{2}{4} = \frac{- 1}{2} \\ CHECK: Substituting x = - \frac{1}{2} in the given equation, we get: \\ LHS= \frac{2 x - 1}{3} - \frac{6 x - 2}{5} \\ = \frac{- 8 x + 1}{15} \\ = \frac{- 8 \times (- \frac{1}{2}) + 1}{15} \\ = \frac{5}{15} \\ = \frac{1}{3} \\ RHS= \frac{1}{3} \\ \begin{array}{l} ∴ LHS=RHS \\ Hence, y= - \frac{1}{2} is a solution of the given equation . \end{array} \end{array}$

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