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Solve the inequality
Answer
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$\dfrac { 2 \left ( x - 1 \right ) } { 3 } - \dfrac { x - 1 } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$\dfrac { 2 \left ( x - 1 \right ) } { 3 } - \dfrac { x - 1 } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
Solution of inequality
$x \geq 3$
$\dfrac{ 2 \left( x-1 \right) }{ 3 } - \dfrac{ x-1 }{ 6 } \leq \dfrac{ 2 }{ 3 } x-1$
$x \geq 3$
$ $ Solve a solution to $ x$
$\dfrac { \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) } { 3 } - \dfrac { x - 1 } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$ $ Multiply each term in parentheses by $ 2$
$\dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { 3 } - \dfrac { x - 1 } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$\color{#FF6800}{ \dfrac { 2 x - 2 } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x - 1 } { 6 } } \leq \dfrac { 2 } { 3 } x - 1$
$ $ Write all numerators above the least common denominator $ $
$\color{#FF6800}{ \dfrac { 4 x - 4 - x + 1 } { 6 } } \leq \dfrac { 2 } { 3 } x - 1$
$\dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 4 \color{#FF6800}{ - } \color{#FF6800}{ x } + 1 } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$ $ Calculate between similar terms $ $
$\dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ x } - 4 + 1 } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$\dfrac { 3 x \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$ $ Add $ - 4 $ and $ 1$
$\dfrac { 3 x \color{#FF6800}{ - } \color{#FF6800}{ 3 } } { 6 } \leq \dfrac { 2 } { 3 } x - 1$
$\dfrac { 3 x - 3 } { 6 } \leq \color{#FF6800}{ \dfrac { 2 } { 3 } } \color{#FF6800}{ x } - 1$
$ $ Calculate the multiplication expression $ $
$\dfrac { 3 x - 3 } { 6 } \leq \color{#FF6800}{ \dfrac { 2 x } { 3 } } - 1$
$\color{#FF6800}{ \dfrac { 3 x - 3 } { 6 } } \leq \color{#FF6800}{ \dfrac { 2 x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \leq \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$3 x - 3 \leq \color{#FF6800}{ 4 } \color{#FF6800}{ x } - 6$
$ $ Move the variable to the left-hand side and change the symbol $ $
$3 x - 3 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \leq - 6$
$3 x \color{#FF6800}{ - } \color{#FF6800}{ 3 } - 4 x \leq - 6$
$ $ Move the constant to the right side and change the sign $ $
$3 x - 4 x \leq - 6 \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \leq - 6 + 3$
$ $ Organize the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } \leq - 6 + 3$
$- x \leq \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$ $ Add $ - 6 $ and $ 3$
$- x \leq \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$\color{#FF6800}{ x } \geq \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
$x \geq \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 3 \right )$
$ $ Simplify Minus $ $
$x \geq 3$
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