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Solve the equation

Answer

Graph

$y = 1.5 x - 0.5 x + 7$

$y = 0.3 x$

$x$Intercept

$\left ( - 7 , 0 \right )$

$y$Intercept

$\left ( 0 , 7 \right )$

$x$Intercept

$\left ( 0 , 0 \right )$

$y$Intercept

$\left ( 0 , 0 \right )$

$x = - 10$

$ $ Solve a solution to $ x$

$\color{#FF6800}{ 1.5 } \color{#FF6800}{ x } - 0.5 x + 7 = 0.3 x$

$ $ Calculate the multiplication expression $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } - 0.5 x + 7 = 0.3 x$

$\dfrac { 3 x } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 0.5 } \color{#FF6800}{ x } + 7 = 0.3 x$

$ $ Calculate the multiplication expression $ $

$\dfrac { 3 x } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + 7 = 0.3 x$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + 7 = 0.3 x$

$ $ Since the denominator is the same as $ 2 $ , combine the fractions into one $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } + 7 = 0.3 x$

$\dfrac { 3 x - x } { 2 } + \color{#FF6800}{ 7 } = 0.3 x$

$ $ Convert an equation to a fraction using $ a=\dfrac{a}{1}$

$\dfrac { 3 x - x } { 2 } + \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } } { \color{#FF6800}{ 1 } } } = 0.3 x$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } } { \color{#FF6800}{ 2 } } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 7 } } { \color{#FF6800}{ 1 } } } = 0.3 x$

$ $ Write all numerators above the least common denominator $ $

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 14 } } { \color{#FF6800}{ 2 } } } = 0.3 x$

$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } + 14 } { 2 } = 0.3 x$

$ $ Calculate between similar terms $ $

$\dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 14 } { 2 } = 0.3 x$

$\dfrac { 2 x + 14 } { 2 } = \color{#FF6800}{ 0.3 } \color{#FF6800}{ x }$

$ $ Calculate the multiplication expression $ $

$\dfrac { 2 x + 14 } { 2 } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } }$

$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 14 } } { \color{#FF6800}{ 2 } } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } } { \color{#FF6800}{ 10 } } }$

$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $

$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 14 } \right ) = \color{#FF6800}{ 3 } \color{#FF6800}{ x }$

$ $ Organize the expression $ $

$\color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 70 }$

$\color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = - 70$

$ $ Organize the expression $ $

$\color{#FF6800}{ 7 } \color{#FF6800}{ x } = - 70$

$\color{#FF6800}{ 7 } \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 70 }$

$ $ Divide both sides by the same number $ $

$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 10 }$

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