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Solve the inequality
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$1 - \left ( 4 + 8 x \right ) \geq - 2 \left ( x - 1 \right ) + 5$
$1 - \left ( 4 + 8 x \right ) \geq - 2 \left ( x - 1 \right ) + 5$
Solution of inequality
$x \leq - \dfrac { 5 } { 3 }$
$1- \left( 4+8x \right) \geq -2 \left( x-1 \right) +5$
$x \leq - \dfrac { 5 } { 3 }$
 Solve a solution to $x$
$1 - \left ( 4 + 8 x \right ) \geq \color{#FF6800}{ - } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) + 5$
 Multiply each term in parentheses by $- 2$
$1 - \left ( 4 + 8 x \right ) \geq \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + \color{#FF6800}{ 2 } + 5$
$1 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \right ) \geq - 2 x + 2 + 5$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$1 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \geq - 2 x + 2 + 5$
$\color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } - 8 x \geq - 2 x + 2 + 5$
 Subtract $4$ from $1$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } - 8 x \geq - 2 x + 2 + 5$
$- 3 - 8 x \geq - 2 x + \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 5 }$
 Add $2$ and $5$
$- 3 - 8 x \geq - 2 x + \color{#FF6800}{ 7 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \geq - 2 x + 7$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \geq - 2 x + 7$
$- 8 x - 3 \geq \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } + 7$
 Move the variable to the left-hand side and change the symbol 
$- 8 x - 3 \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq 7$
$- 8 x \color{#FF6800}{ - } \color{#FF6800}{ 3 } + 2 x \geq 7$
 Move the constant to the right side and change the sign 
$- 8 x + 2 x \geq 7 \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq 7 + 3$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \geq 7 + 3$
$- 6 x \geq \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
 Add $7$ and $3$
$- 6 x \geq \color{#FF6800}{ 10 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 10 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$6 x \leq - 10$
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 10 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 5 } { 3 } }$
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