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Solve the equation
Answer
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Graph
$y = 5 \left ( - 1 + 2 x \right ) + 3 \left ( 4 - x \right )$
$y = 0$
$x$Intercept
$\left ( - 1 , 0 \right )$
$y$Intercept
$\left ( 0 , 7 \right )$
$x = - 1$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) + 3 \left ( 4 - x \right ) = 0$
$ $ Multiply each term in parentheses by $ 5$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } + \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 3 \left ( 4 - x \right ) = 0$
$- 5 + 5 \times 2 x + \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = 0$
$ $ Multiply each term in parentheses by $ 3$
$- 5 + 5 \times 2 x + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 0$
$- 5 + \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 3 \times 4 - 3 x = 0$
$ $ Simplify the expression $ $
$- 5 + \color{#FF6800}{ 10 } \color{#FF6800}{ x } + 3 \times 4 - 3 x = 0$
$- 5 + 10 x + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } - 3 x = 0$
$ $ Multiply $ 3 $ and $ 4$
$- 5 + 10 x + \color{#FF6800}{ 12 } - 3 x = 0$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } + 10 x \color{#FF6800}{ + } \color{#FF6800}{ 12 } - 3 x = 0$
$ $ Add $ - 5 $ and $ 12$
$\color{#FF6800}{ 7 } + 10 x - 3 x = 0$
$7 + \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 0$
$ $ Calculate between similar terms $ $
$7 + \color{#FF6800}{ 7 } \color{#FF6800}{ x } = 0$
$\color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ x } = 0$
$ $ Organize the expression $ $
$\color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 7 } = 0$
$7 x \color{#FF6800}{ + } \color{#FF6800}{ 7 } = 0$
$ $ Move the constant to the right side and change the sign $ $
$7 x = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$\color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
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