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Formula
Solve the inequality
Graph
$0.4 x - 1.5 \geq 0.2 x - 0.7$
$0.4 x - 1.5 \geq 0.2 x - 0.7$
Solution of inequality
$x \geq 4$
$0.4x-1.5 \geq 0.2x-0.7$
$x \geq 4$
 Solve a solution to $x$
$\color{#FF6800}{ 0.4 } \color{#FF6800}{ x } - 1.5 \geq 0.2 x - 0.7$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { 2 x } { 5 } } - 1.5 \geq 0.2 x - 0.7$
$\dfrac { 2 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 1.5 } \geq 0.2 x - 0.7$
 Convert decimals to fractions 
$\dfrac { 2 x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \geq 0.2 x - 0.7$
$\dfrac { 2 x } { 5 } - \dfrac { 3 } { 2 } \geq \color{#FF6800}{ 0.2 } \color{#FF6800}{ x } - 0.7$
 Calculate the multiplication expression 
$\dfrac { 2 x } { 5 } - \dfrac { 3 } { 2 } \geq \color{#FF6800}{ \dfrac { x } { 5 } } - 0.7$
$\dfrac { 2 x } { 5 } - \dfrac { 3 } { 2 } \geq \dfrac { x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ 0.7 }$
 Convert decimals to fractions 
$\dfrac { 2 x } { 5 } - \dfrac { 3 } { 2 } \geq \dfrac { x } { 5 } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 10 } }$
$\color{#FF6800}{ \dfrac { 2 x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \geq \color{#FF6800}{ \dfrac { x } { 5 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 7 } { 10 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 15 } { 2 } } \geq \color{#FF6800}{ \dfrac { 2 x - 7 } { 2 } }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 15 } { 2 } } \geq \color{#FF6800}{ \dfrac { 2 x - 7 } { 2 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 15 } \geq \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 7 }$
$4 x - 15 \geq \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 7$
 Move the variable to the left-hand side and change the symbol 
$4 x - 15 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq - 7$
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 15 } - 2 x \geq - 7$
 Move the constant to the right side and change the sign 
$4 x - 2 x \geq - 7 \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq - 7 + 15$
 Organize the expression 
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq - 7 + 15$
$2 x \geq \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 15 }$
 Add $- 7$ and $15$
$2 x \geq \color{#FF6800}{ 8 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 8 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ 4 }$
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