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Solve the inequality
Answer
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$2 \left ( 2 x + 1 \right ) - 6 \left ( x + 3 \right ) \leq 0$
$2 \left ( 2 x + 1 \right ) - 6 \left ( x + 3 \right ) \leq 0$
Solution of inequality
$x \geq - 8$
$2(2x+1)-6(x+3)\leq0$
$x \geq - 8$
$ $ Solve a solution to $ x$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - 6 \left ( x + 3 \right ) \leq 0$
$ $ Multiply each term in parentheses by $ 2$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \color{#FF6800}{ 2 } - 6 \left ( x + 3 \right ) \leq 0$
$2 \times 2 x + 2 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \leq 0$
$ $ Multiply each term in parentheses by $ - 6$
$2 \times 2 x + 2 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \leq 0$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 2 - 6 x - 6 \times 3 \leq 0$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } + 2 - 6 x - 6 \times 3 \leq 0$
$4 x + 2 - 6 x \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \leq 0$
$ $ Multiply $ - 6 $ and $ 3$
$4 x + 2 - 6 x \color{#FF6800}{ - } \color{#FF6800}{ 18 } \leq 0$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } + 2 \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } - 18 \leq 0$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 2 - 18 \leq 0$
$- 2 x + \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 18 } \leq 0$
$ $ Subtract $ 18 $ from $ 2$
$- 2 x \color{#FF6800}{ - } \color{#FF6800}{ 16 } \leq 0$
$- 2 x \color{#FF6800}{ - } \color{#FF6800}{ 16 } \leq 0$
$ $ Move the constant to the right side and change the sign $ $
$- 2 x \leq \color{#FF6800}{ 16 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq \color{#FF6800}{ 16 }$
$ $ Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction $ $
$2 x \geq - 16$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 16 }$
$ $ Divide both sides by the same number $ $
$\color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
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