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Formula
Solve the inequality
Graph
$0.5 \left ( x - 2 \right ) \leq 0.7 x - 1.2$
$0.5 \left ( x - 2 \right ) \leq 0.7 x - 1.2$
Solution of inequality
$x \geq 1$
$0.5 \left( x-2 \right) \leq 0.7x-1.2$
$x \geq 1$
 Solve a solution to $x$
$\color{#FF6800}{ 0.5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \leq 0.7 x - 1.2$
 Multiply each term in parentheses by $0.5$
$\color{#FF6800}{ 0.5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 0.5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \leq 0.7 x - 1.2$
$\color{#FF6800}{ 0.5 } \color{#FF6800}{ x } + 0.5 \times \left ( - 2 \right ) \leq 0.7 x - 1.2$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { x } { 2 } } + 0.5 \times \left ( - 2 \right ) \leq 0.7 x - 1.2$
$\dfrac { x } { 2 } + \color{#FF6800}{ 0.5 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \leq 0.7 x - 1.2$
 Multiply $0.5$ and $- 2$
$\dfrac { x } { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \leq 0.7 x - 1.2$
$\dfrac { x } { 2 } - 1 \leq \color{#FF6800}{ 0.7 } \color{#FF6800}{ x } - 1.2$
 Calculate the multiplication expression 
$\dfrac { x } { 2 } - 1 \leq \color{#FF6800}{ \dfrac { 7 x } { 10 } } - 1.2$
$\dfrac { x } { 2 } - 1 \leq \dfrac { 7 x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ 1.2 }$
 Convert decimals to fractions 
$\dfrac { x } { 2 } - 1 \leq \dfrac { 7 x } { 10 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 6 } { 5 } }$
$\color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \leq \color{#FF6800}{ \dfrac { 7 x } { 10 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 6 } { 5 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 10 } \leq \color{#FF6800}{ 7 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$5 x - 10 \leq \color{#FF6800}{ 7 } \color{#FF6800}{ x } - 12$
 Move the variable to the left-hand side and change the symbol 
$5 x - 10 \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \leq - 12$
$5 x \color{#FF6800}{ - } \color{#FF6800}{ 10 } - 7 x \leq - 12$
 Move the constant to the right side and change the sign 
$5 x - 7 x \leq - 12 \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ x } \leq - 12 + 10$
 Organize the expression 
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq - 12 + 10$
$- 2 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
 Add $- 12$ and $10$
$- 2 x \leq \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \leq \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$2 x \geq 2$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 2 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ 1 }$
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Inequality
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