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Solve the equation
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$2 \left( x-2 \right) : 5 = \left( x-1 \right) : 3$
$x = 7$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) : \color{#FF6800}{ 5 } = \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } : \color{#FF6800}{ 3 }$
$a:b=c:d $ of proportional expression equals to $ a\times d = b\times c$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$2 \left ( x - 2 \right ) \times 3 = \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$ $ Multiply each term in parentheses by $ 5$
$2 \left ( x - 2 \right ) \times 3 = \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 3 } = 5 x - 5$
$ $ Organize the expression $ $
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } = 5 x - 5$
$6 x - 12 = \color{#FF6800}{ 5 } \color{#FF6800}{ x } - \color{#FF6800}{ 5 }$
$ $ Move the variable to the left-hand side and change the symbol $ $
$6 x - 12 \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } = - 5$
$6 x \color{#FF6800}{ - } \color{#FF6800}{ 12 } - 5 x = - 5$
$ $ Move the constant to the right side and change the sign $ $
$6 x - 5 x = - 5 \color{#FF6800}{ + } \color{#FF6800}{ 12 }$
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } = - 5 + 12$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = - 5 + 12$
$x = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 12 }$
$ $ Add $ - 5 $ and $ 12$
$x = \color{#FF6800}{ 7 }$
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