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Solve the inequality
Answer
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$- \left ( x - 3 \right ) \leq 3 \left ( x - 1 \right )$
$- \left ( x - 3 \right ) \leq 3 \left ( x - 1 \right )$
Solution of inequality
$x \geq \dfrac { 3 } { 2 }$
$x \geq \dfrac { 3 } { 2 }$
$ $ 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 $ $
$\color{#FF6800}{ x } \geq \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 2 } } }$
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