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Formula
Solve the inequality
Graph
$1.2 x + 0.5 \geq 0.8 x - 2.7$
$1.2 x + 0.5 \geq 0.8 x - 2.7$
Solution of inequality
$x \geq - 8$
$1.2x+0.5 \geq 0.8x-2.7$
$x \geq - 8$
 Solve a solution to $x$
$\color{#FF6800}{ 1.2 } \color{#FF6800}{ x } + 0.5 \geq 0.8 x - 2.7$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { 6 x } { 5 } } + 0.5 \geq 0.8 x - 2.7$
$\dfrac { 6 x } { 5 } + \color{#FF6800}{ 0.5 } \geq 0.8 x - 2.7$
 Convert decimals to fractions 
$\dfrac { 6 x } { 5 } + \color{#FF6800}{ \dfrac { 1 } { 2 } } \geq 0.8 x - 2.7$
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \color{#FF6800}{ 0.8 } \color{#FF6800}{ x } - 2.7$
 Calculate the multiplication expression 
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \color{#FF6800}{ \dfrac { 4 x } { 5 } } - 2.7$
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \dfrac { 4 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2.7 }$
 Convert decimals to fractions 
$\dfrac { 6 x } { 5 } + \dfrac { 1 } { 2 } \geq \dfrac { 4 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 } { 10 } }$
$\color{#FF6800}{ \dfrac { 6 x } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } \geq \color{#FF6800}{ \dfrac { 4 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 27 } { 10 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \geq \color{#FF6800}{ \dfrac { 8 x - 27 } { 2 } }$
$\color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 5 } { 2 } } \geq \color{#FF6800}{ \dfrac { 8 x - 27 } { 2 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \geq \color{#FF6800}{ 8 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 27 }$
$12 x + 5 \geq \color{#FF6800}{ 8 } \color{#FF6800}{ x } - 27$
 Move the variable to the left-hand side and change the symbol 
$12 x + 5 \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \geq - 27$
$12 x \color{#FF6800}{ + } \color{#FF6800}{ 5 } - 8 x \geq - 27$
 Move the constant to the right side and change the sign 
$12 x - 8 x \geq - 27 \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
$\color{#FF6800}{ 12 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 8 } \color{#FF6800}{ x } \geq - 27 - 5$
 Organize the expression 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq - 27 - 5$
$4 x \geq \color{#FF6800}{ - } \color{#FF6800}{ 27 } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
 Find the sum of the negative numbers 
$4 x \geq \color{#FF6800}{ - } \color{#FF6800}{ 32 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 32 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 8 }$
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Inequality
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