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x - (x-1)/(2) = 1 - (x-2)/(3)Solve

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\begin{gathered} \; \color{pink}{\frak{\qquad \: x - (x - 1)/(2) = 1 - (x - 2)/(3)}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{((2 * x) - x - 1)/(2) = ((3 * 1) - x - 2)/(3)}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{(2x - x - 1)/(2) = (3 - x - 2)/(3)}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{(x - 1)/(2) = (1 - x)/(3)}} \\ \end{gathered}

Cross Multiplying,,


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3(x - 1) = 2(1 - x)}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x - 3 = 2 - 2x}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x + 2x = 2 + 3}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{5x = 5}} \\ \\ \end{gathered}


\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{x = \frac{\cancel{ \: 5}}{\cancel{ \: 5}}}} \\ \\ \end{gathered}


\begin{gathered} \; \color{cyan}{\hookrightarrow \: \underline{\boxed{\frak{x = 1}}}} \: \pmb{\bigstar} \\ \\ \end{gathered}


\begin{gathered} \qquad{\qquad{\pmb{━━━━━ღ◆ღ━━━━━}}} \end{gathered}

User Salil Rajkarnikar
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