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Formula
Solve the inequality
Graph
$5 \left ( 6 - 2 x \right ) > 4 \left ( 3 - 2 x \right )$
$5 \left ( 6 - 2 x \right ) > 4 \left ( 3 - 2 x \right )$
Solution of inequality
$x < 9$
$5 \left( 6-2x \right) > 4 \left( 3-2x \right)$
$x < 9$
 Solve a solution to $x$
$\color{#FF6800}{ 5 } \left ( \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) > 4 \left ( 3 - 2 x \right )$
 Multiply each term in parentheses by $5$
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x } > 4 \left ( 3 - 2 x \right )$
$5 \times 6 + 5 \times \left ( - 2 \right ) x > \color{#FF6800}{ 4 } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right )$
 Multiply each term in parentheses by $4$
$5 \times 6 + 5 \times \left ( - 2 \right ) x > \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 6 } + 5 \times \left ( - 2 \right ) x > 4 \times 3 + 4 \times \left ( - 2 \right ) x$
 Multiply $5$ and $6$
$\color{#FF6800}{ 30 } + 5 \times \left ( - 2 \right ) x > 4 \times 3 + 4 \times \left ( - 2 \right ) x$
$30 + \color{#FF6800}{ 5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x } > 4 \times 3 + 4 \times \left ( - 2 \right ) x$
 Simplify the expression 
$30 \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ x } > 4 \times 3 + 4 \times \left ( - 2 \right ) x$
$30 - 10 x > \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } + 4 \times \left ( - 2 \right ) x$
 Multiply $4$ and $3$
$30 - 10 x > \color{#FF6800}{ 12 } + 4 \times \left ( - 2 \right ) x$
$30 - 10 x > 12 + \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x }$
 Simplify the expression 
$30 - 10 x > 12 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x }$
$\color{#FF6800}{ 30 } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ x } > 12 - 8 x$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 30 } > 12 - 8 x$
$- 10 x + 30 > \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x }$
 Organize the expression 
$- 10 x + 30 > \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 12 }$
$- 10 x + 30 > \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } + 12$
 Move the variable to the left-hand side and change the symbol 
$- 10 x + 30 \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ x } > 12$
$- 10 x \color{#FF6800}{ + } \color{#FF6800}{ 30 } + 8 x > 12$
 Move the constant to the right side and change the sign 
$- 10 x + 8 x > 12 \color{#FF6800}{ - } \color{#FF6800}{ 30 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ x } > 12 - 30$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } > 12 - 30$
$- 2 x > \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 30 }$
 Subtract $30$ from $12$
$- 2 x > \color{#FF6800}{ - } \color{#FF6800}{ 18 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } > \color{#FF6800}{ - } \color{#FF6800}{ 18 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$2 x < 18$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } < \color{#FF6800}{ 18 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } < \color{#FF6800}{ 9 }$
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Inequality
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