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Formula
Solve the equation
$9u-8v = 4$
$u = \dfrac { 8 } { 9 } v + \dfrac { 4 } { 9 }$
 Solve a solution to $u$
$9 u \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } = 4$
 Move the rest of the expression except $u$ term to the right side and replace the sign 
$9 u - 8 v \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } \right ) = 4 \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } \right )$
$\color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } \right ) = 4 - \left ( - 8 v \right )$
 Organize the expression 
$\color{#FF6800}{ 9 } \color{#FF6800}{ u } = 4 - \left ( - 8 v \right )$
$9 u = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } \right )$
 Organize the expression 
$9 u = \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ 9 } \color{#FF6800}{ u } = \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
 Divide both sides by the same number 
$\color{#FF6800}{ u } = \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 9 }$
$u = \left ( 8 v + 4 \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 9 }$
 Convert division to multiplication 
$u = \left ( 8 v + 4 \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 9 } }$
$u = \left ( \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 9 } }$
 Multiply each term in parentheses by $\dfrac { 1 } { 9 }$
$u = \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 9 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 9 } }$
$u = \color{#FF6800}{ 8 } \color{#FF6800}{ v } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 9 } } + 4 \times \dfrac { 1 } { 9 }$
 Simplify the expression 
$u = \color{#FF6800}{ \dfrac { 8 } { 9 } } \color{#FF6800}{ v } + 4 \times \dfrac { 1 } { 9 }$
$u = \dfrac { 8 } { 9 } v + \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 9 } }$
 Calculate the product of rational numbers 
$u = \dfrac { 8 } { 9 } v + \color{#FF6800}{ \dfrac { 4 } { 9 } }$
$v = \dfrac { 9 } { 8 } u - \dfrac { 1 } { 2 }$
 Solve a solution to $v$
$\color{#FF6800}{ 9 } \color{#FF6800}{ u } - 8 v = 4$
 Move the rest of the expression except $v$ term to the right side and replace the sign 
$- 8 v = 4 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ u } \right )$
$- 8 v = \color{#FF6800}{ 4 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ u } \right )$
 Organize the expression 
$- 8 v = \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ v } = \color{#FF6800}{ - } \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
 Change the sign of both sides of the equation 
$8 v = 9 u - 4$
$\color{#FF6800}{ 8 } \color{#FF6800}{ v } = \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
 Divide both sides by the same number 
$\color{#FF6800}{ v } = \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 8 }$
$v = \left ( 9 u - 4 \right ) \color{#FF6800}{ \div } \color{#FF6800}{ 8 }$
 Convert division to multiplication 
$v = \left ( 9 u - 4 \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 8 } }$
$v = \left ( \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 8 } }$
 Multiply each term in parentheses by $\dfrac { 1 } { 8 }$
$v = \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 8 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 8 } }$
$v = \color{#FF6800}{ 9 } \color{#FF6800}{ u } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 8 } } - 4 \times \dfrac { 1 } { 8 }$
 Simplify the expression 
$v = \color{#FF6800}{ \dfrac { 9 } { 8 } } \color{#FF6800}{ u } - 4 \times \dfrac { 1 } { 8 }$
$v = \dfrac { 9 } { 8 } u \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 8 } }$
 Calculate the product of rational numbers 
$v = \dfrac { 9 } { 8 } u \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
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