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Formula
Solve the inequality
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$- 0.7 + \dfrac { 1 } { 5 } \left ( 2 - x \right ) \leq - 0.3 \left ( x - 2 \right )$
$- 0.7 + \dfrac { 1 } { 5 } \left ( 2 - x \right ) \leq - 0.3 \left ( x - 2 \right )$
Solution of inequality
$x \leq 9$
$-0.7+ \dfrac{ 1 }{ 5 } \left( 2-x \right) \leq -0.3 \left( x-2 \right)$
$x \leq 9$
 Solve a solution to $x$
$- 0.7 + \color{#FF6800}{ \dfrac { 1 } { 5 } } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \leq - 0.3 \left ( x - 2 \right )$
 Multiply each term in parentheses by $\dfrac { 1 } { 5 }$
$- 0.7 + \color{#FF6800}{ \dfrac { 1 } { 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } \color{#FF6800}{ x } \leq - 0.3 \left ( x - 2 \right )$
$- 0.7 + \dfrac { 1 } { 5 } \times 2 - \dfrac { 1 } { 5 } x \leq \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
 Multiply each term in parentheses by $- 0.3$
$- 0.7 + \dfrac { 1 } { 5 } \times 2 - \dfrac { 1 } { 5 } x \leq \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$\color{#FF6800}{ - } \color{#FF6800}{ 0.7 } + \dfrac { 1 } { 5 } \times 2 - \dfrac { 1 } { 5 } x \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
 Convert decimals to fractions 
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 10 } } + \dfrac { 1 } { 5 } \times 2 - \dfrac { 1 } { 5 } x \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
$- \dfrac { 7 } { 10 } + \color{#FF6800}{ \dfrac { 1 } { 5 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } - \dfrac { 1 } { 5 } x \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
 Calculate the product of rational numbers 
$- \dfrac { 7 } { 10 } + \color{#FF6800}{ \dfrac { 2 } { 5 } } - \dfrac { 1 } { 5 } x \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
$- \dfrac { 7 } { 10 } + \dfrac { 2 } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 5 } } \color{#FF6800}{ x } \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
 Calculate the multiplication expression 
$- \dfrac { 7 } { 10 } + \dfrac { 2 } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 5 } } \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 10 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 2 } { 5 } } - \dfrac { x } { 5 } \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
 Find the sum or difference of the fractions 
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 10 } } - \dfrac { x } { 5 } \leq - 0.3 x - 0.3 \times \left ( - 2 \right )$
$- \dfrac { 3 } { 10 } - \dfrac { x } { 5 } \leq \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ x } - 0.3 \times \left ( - 2 \right )$
 Calculate the multiplication expression 
$- \dfrac { 3 } { 10 } - \dfrac { x } { 5 } \leq \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 x } { 10 } } - 0.3 \times \left ( - 2 \right )$
$- \dfrac { 3 } { 10 } - \dfrac { x } { 5 } \leq - \dfrac { 3 x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ 0.3 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
 Multiply $- 0.3$ and $- 2$
$- \dfrac { 3 } { 10 } - \dfrac { x } { 5 } \leq - \dfrac { 3 x } { 10 } + \color{#FF6800}{ 0.6 }$
$- \dfrac { 3 } { 10 } - \dfrac { x } { 5 } \leq - \dfrac { 3 x } { 10 } + \color{#FF6800}{ 0.6 }$
 Convert decimals to fractions 
$- \dfrac { 3 } { 10 } - \dfrac { x } { 5 } \leq - \dfrac { 3 x } { 10 } + \color{#FF6800}{ \dfrac { 3 } { 5 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 10 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 5 } } \leq \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 x } { 10 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 5 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \leq \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$- 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \leq - 3 x + 6$
 Get rid of unnecessary parentheses 
$- 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq - 3 x + 6$
$- 3 - 2 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 6$
 Move the variable to the left-hand side and change the symbol 
$- 3 - 2 x \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \leq 6$
$\color{#FF6800}{ - } \color{#FF6800}{ 3 } - 2 x + 3 x \leq 6$
 Move the constant to the right side and change the sign 
$- 2 x + 3 x \leq 6 \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \leq 6 + 3$
 Organize the expression 
$\color{#FF6800}{ x } \leq 6 + 3$
$x \leq \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
 Add $6$ and $3$
$x \leq \color{#FF6800}{ 9 }$
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