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Solve the inequality
Graph
$\dfrac { 1 } { 2 } x - \dfrac { 2 - x } { 3 } \leq \dfrac { 1 } { 6 }$
$\dfrac { 1 } { 2 } x - \dfrac { 2 - x } { 3 } \leq \dfrac { 1 } { 6 }$
Solution of inequality
$x \leq 1$
$\dfrac{ 1 }{ 2 } x- \dfrac{ 2-x }{ 3 } \leq \dfrac{ 1 }{ 6 }$
$x \leq 1$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } - \dfrac { 2 - x } { 3 } \leq \dfrac { 1 } { 6 }$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { x } { 2 } } - \dfrac { 2 - x } { 3 } \leq \dfrac { 1 } { 6 }$
$\dfrac { x } { 2 } - \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } } { 3 } \leq \dfrac { 1 } { 6 }$
 Organize the expression 
$\dfrac { x } { 2 } - \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } { 3 } \leq \dfrac { 1 } { 6 }$
$\color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { - x + 2 } { 3 } } \leq \color{#FF6800}{ \dfrac { 1 } { 6 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \right ) \leq \color{#FF6800}{ 1 }$
$3 x - \left ( \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \right ) \leq 1$
 Multiply each term in parentheses by $2$
$3 x - \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \right ) \leq 1$
$3 x - \left ( - 2 x + \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \right ) \leq 1$
 Multiply $2$ and $2$
$3 x - \left ( - 2 x + \color{#FF6800}{ 4 } \right ) \leq 1$
$3 x \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \leq 1$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$3 x + \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \leq 1$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 4 \leq 1$
 Calculate between similar terms 
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } - 4 \leq 1$
$5 x \color{#FF6800}{ - } \color{#FF6800}{ 4 } \leq 1$
 Move the constant to the right side and change the sign 
$5 x \leq 1 \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
$5 x \leq \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
 Add $1$ and $4$
$5 x \leq \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \leq \color{#FF6800}{ 5 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \leq \color{#FF6800}{ 1 }$
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