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Formula
Solve the inequality
Graph
$- \left ( x - 3 \right ) \leq 3 \left ( x - 1 \right )$
$- \left ( x - 3 \right ) \leq 3 \left ( x - 1 \right )$
Solution of inequality
$x \geq \dfrac { 3 } { 2 }$
$- \left( x-3 \right) \leq 3 \left( x-1 \right)$
$x \geq \dfrac { 3 } { 2 }$
 Solve a solution to $x$
$- \left ( x - 3 \right ) \leq \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
 Multiply each term in parentheses by $3$
$- \left ( x - 3 \right ) \leq \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \leq 3 x - 3$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \leq 3 x - 3$
$- x + 3 \leq \color{#FF6800}{ 3 } \color{#FF6800}{ x } - \color{#FF6800}{ 3 }$
 Move the variable to the left-hand side and change the symbol 
$- x + 3 \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \leq - 3$
$- x \color{#FF6800}{ + } \color{#FF6800}{ 3 } - 3 x \leq - 3$
 Move the constant to the right side and change the sign 
$- x - 3 x \leq - 3 \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \leq - 3 - 3$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \leq - 3 - 3$
$- 4 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
 Find the sum of the negative numbers 
$- 4 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$4 x \geq 6$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 6 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ \dfrac { 3 } { 2 } }$
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