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Formula
Solve the equation
Graph
$y = x + 0. \dot{ 2 } \dot{ 9 }$
$y = 0. \dot{ 8 } x + 1. \dot{ 0 } \dot{ 7 }$
$x$Intercept
$\left ( - \dfrac { 29 } { 99 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 29 } { 99 } \right )$
$x$Intercept
$\left ( - \dfrac { 53 } { 44 } , 0 \right )$
$y$Intercept
$\left ( 0 , \dfrac { 106 } { 99 } \right )$
$x+0. \dot{ 2 } \dot{ 9 } = 0. \dot{ 8 } x+1. \dot{ 0 } \dot{ 7 }$
$x = 7$
 Solve a solution to $x$
$x + \color{#FF6800}{ 0. \dot{ 2 } \dot{ 9 } } = 0. \dot{ 8 } x + 1. \dot{ 0 } \dot{ 7 }$
 Convert the repeating decimal number to a fraction 
$x + \color{#FF6800}{ \dfrac { 29 } { 99 } } = 0. \dot{ 8 } x + 1. \dot{ 0 } \dot{ 7 }$
$x + \dfrac { 29 } { 99 } = \color{#FF6800}{ 0. \dot{ 8 } } x + 1. \dot{ 0 } \dot{ 7 }$
 Convert the repeating decimal number to a fraction 
$x + \dfrac { 29 } { 99 } = \color{#FF6800}{ \dfrac { 8 } { 9 } } x + 1. \dot{ 0 } \dot{ 7 }$
$x + \dfrac { 29 } { 99 } = \color{#FF6800}{ \dfrac { 8 } { 9 } } \color{#FF6800}{ x } + 1. \dot{ 0 } \dot{ 7 }$
 Calculate the multiplication expression 
$x + \dfrac { 29 } { 99 } = \color{#FF6800}{ \dfrac { 8 x } { 9 } } + 1. \dot{ 0 } \dot{ 7 }$
$x + \dfrac { 29 } { 99 } = \dfrac { 8 x } { 9 } + \color{#FF6800}{ 1. \dot{ 0 } \dot{ 7 } }$
 Convert the repeating decimal number to a fraction 
$x + \dfrac { 29 } { 99 } = \dfrac { 8 x } { 9 } + \color{#FF6800}{ \dfrac { 106 } { 99 } }$
$\color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 29 } { 99 } } = \color{#FF6800}{ \dfrac { 8 x } { 9 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 106 } { 99 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 29 } { 11 } } = \color{#FF6800}{ \dfrac { 88 x + 106 } { 11 } }$
$\color{#FF6800}{ 9 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 29 } { 11 } } = \color{#FF6800}{ \dfrac { 88 x + 106 } { 11 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 29 } = \color{#FF6800}{ 88 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 106 }$
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 29 } = \color{#FF6800}{ 88 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 106 }$
 Organize the expression 
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 88 } \color{#FF6800}{ x } = \color{#FF6800}{ 106 } \color{#FF6800}{ - } \color{#FF6800}{ 29 }$
$\color{#FF6800}{ 99 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 88 } \color{#FF6800}{ x } = 106 - 29$
 Organize the expression 
$\color{#FF6800}{ 11 } \color{#FF6800}{ x } = 106 - 29$
$11 x = \color{#FF6800}{ 106 } \color{#FF6800}{ - } \color{#FF6800}{ 29 }$
 Subtract $29$ from $106$
$11 x = \color{#FF6800}{ 77 }$
$\color{#FF6800}{ 11 } \color{#FF6800}{ x } = \color{#FF6800}{ 77 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } = \color{#FF6800}{ 7 }$
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