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Formula
Solve the inequality
Graph
$\dfrac { x } { 3 } - \dfrac { x - 4 } { 2 } \leq 3$
$\dfrac { x } { 3 } - \dfrac { x - 4 } { 2 } \leq 3$
Solution of inequality
$x \geq - 6$
$\dfrac{ x }{ 3 } - \dfrac{ x-4 }{ 2 } \leq 3$
$x \geq - 6$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 4 } { 2 } } \leq \color{#FF6800}{ 3 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \right ) \leq \color{#FF6800}{ 18 }$
$2 x - \left ( \color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \right ) \leq 18$
 Multiply each term in parentheses by $3$
$2 x - \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \right ) \leq 18$
$2 x - \left ( 3 x + \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \right ) \leq 18$
 Multiply $3$ and $- 4$
$2 x - \left ( 3 x \color{#FF6800}{ - } \color{#FF6800}{ 12 } \right ) \leq 18$
$2 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 } \right ) \leq 18$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$2 x \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + \color{#FF6800}{ 12 } \leq 18$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 12 \leq 18$
 Calculate between similar terms 
$\color{#FF6800}{ - } \color{#FF6800}{ x } + 12 \leq 18$
$- x \color{#FF6800}{ + } \color{#FF6800}{ 12 } \leq 18$
 Move the constant to the right side and change the sign 
$- x \leq 18 \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$- x \leq \color{#FF6800}{ 18 } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
 Subtract $12$ from $18$
$- x \leq \color{#FF6800}{ 6 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } \leq \color{#FF6800}{ 6 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
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