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Solve the equation
Answer
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Graph
$y = 15 x - 10$
$y = 6 x - \left ( x + 2 \right ) + \left ( - x + 3 \right )$
$x$Intercept
$\left ( \dfrac { 2 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , - 10 \right )$
$x$Intercept
$\left ( - \dfrac { 1 } { 4 } , 0 \right )$
$y$Intercept
$\left ( 0 , 1 \right )$
$15x-10 = 6x- \left( x+2 \right) + \left( -x+3 \right)$
$x = 1$
$ $ Solve a solution to $ x$
$15 x - 10 = 6 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) + \left ( - x + 3 \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$15 x - 10 = 6 x \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } + \left ( - x + 3 \right )$
$15 x - 10 = \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
$ $ Get rid of unnecessary parentheses $ $
$15 x - 10 = \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$15 x - 10 = \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } - 2 \color{#FF6800}{ - } \color{#FF6800}{ x } + 3$
$ $ Calculate between similar terms $ $
$15 x - 10 = \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 2 + 3$
$15 x - 10 = 4 x \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Add $ - 2 $ and $ 3$
$15 x - 10 = 4 x + \color{#FF6800}{ 1 }$
$15 x - 10 = \color{#FF6800}{ 4 } \color{#FF6800}{ x } + 1$
$ $ Move the variable to the left-hand side and change the symbol $ $
$15 x - 10 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = 1$
$15 x \color{#FF6800}{ - } \color{#FF6800}{ 10 } - 4 x = 1$
$ $ Move the constant to the right side and change the sign $ $
$15 x - 4 x = 1 \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$\color{#FF6800}{ 15 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = 1 + 10$
$ $ Organize the expression $ $
$\color{#FF6800}{ 11 } \color{#FF6800}{ x } = 1 + 10$
$11 x = \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$ $ Add $ 1 $ and $ 10$
$11 x = \color{#FF6800}{ 11 }$
$\color{#FF6800}{ 11 } \color{#FF6800}{ x } = \color{#FF6800}{ 11 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 1 }$
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