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Solve the equation
Answer
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Graph
$y = 0.12 x + 2.6$
$y = 0.01 x + 0.4$
$x$Intercept
$\left ( - \dfrac { 65 } { 3 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 13 } { 5 } \right )$
$x$Intercept
$\left ( - 40 , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 2 } { 5 } \right )$
$0.12x+2.6 = 0.01x+0.4$
$x = - 20$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 0.12 } \color{#FF6800}{ x } + 2.6 = 0.01 x + 0.4$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { 3 x } { 25 } } + 2.6 = 0.01 x + 0.4$
$\dfrac { 3 x } { 25 } + \color{#FF6800}{ 2.6 } = 0.01 x + 0.4$
$ $ Convert decimals to fractions $ $
$\dfrac { 3 x } { 25 } + \color{#FF6800}{ \dfrac { 13 } { 5 } } = 0.01 x + 0.4$
$\dfrac { 3 x } { 25 } + \dfrac { 13 } { 5 } = \color{#FF6800}{ 0.01 } \color{#FF6800}{ x } + 0.4$
$ $ Calculate the multiplication expression $ $
$\dfrac { 3 x } { 25 } + \dfrac { 13 } { 5 } = \color{#FF6800}{ \dfrac { x } { 100 } } + 0.4$
$\dfrac { 3 x } { 25 } + \dfrac { 13 } { 5 } = \dfrac { x } { 100 } + \color{#FF6800}{ 0.4 }$
$ $ Convert decimals to fractions $ $
$\dfrac { 3 x } { 25 } + \dfrac { 13 } { 5 } = \dfrac { x } { 100 } + \color{#FF6800}{ \dfrac { 2 } { 5 } }$
$\color{#FF6800}{ \dfrac { 3 x } { 25 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 13 } { 5 } } = \color{#FF6800}{ \dfrac { x } { 100 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 2 } { 5 } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 4 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 260 } = \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 40 }$
$\color{#FF6800}{ 4 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 260 } = \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 40 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 40 } \color{#FF6800}{ - } \color{#FF6800}{ 260 }$
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } = 40 - 260$
$ $ Organize the expression $ $
$\color{#FF6800}{ 11 } \color{#FF6800}{ x } = 40 - 260$
$11 x = \color{#FF6800}{ 40 } \color{#FF6800}{ - } \color{#FF6800}{ 260 }$
$ $ Subtract $ 260 $ from $ 40$
$11 x = \color{#FF6800}{ - } \color{#FF6800}{ 220 }$
$\color{#FF6800}{ 11 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 220 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 20 }$
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