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Formula
Solve the inequality
Graph
$\dfrac { 2 } { 3 } x - 3 \geq 1 + \dfrac { 1 } { 6 } x$
$\dfrac { 2 } { 3 } x - 3 \geq 1 + \dfrac { 1 } { 6 } x$
Solution of inequality
$x \geq 8$
$\dfrac{ 2 }{ 3 } x-3 \geq 1+ \dfrac{ 1 }{ 6 } x$
$x \geq 8$
 Solve a solution to $x$
$\color{#FF6800}{ \dfrac { 2 } { 3 } } \color{#FF6800}{ x } - 3 \geq 1 + \dfrac { 1 } { 6 } x$
 Calculate the multiplication expression 
$\color{#FF6800}{ \dfrac { 2 x } { 3 } } - 3 \geq 1 + \dfrac { 1 } { 6 } x$
$\dfrac { 2 x } { 3 } - 3 \geq 1 + \color{#FF6800}{ \dfrac { 1 } { 6 } } \color{#FF6800}{ x }$
 Calculate the multiplication expression 
$\dfrac { 2 x } { 3 } - 3 \geq 1 + \color{#FF6800}{ \dfrac { x } { 6 } }$
$\color{#FF6800}{ \dfrac { 2 x } { 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \geq \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { x } { 6 } }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ - } \color{#FF6800}{ 18 } \geq \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 6 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) - 18 \geq x + 6$
 Get rid of unnecessary parentheses 
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 18 \geq x + 6$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } - 18 \geq x + 6$
 Simplify the expression 
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } - 18 \geq x + 6$
$4 x - 18 \geq \color{#FF6800}{ x } + 6$
 Move the variable to the left-hand side and change the symbol 
$4 x - 18 \color{#FF6800}{ - } \color{#FF6800}{ x } \geq 6$
$4 x \color{#FF6800}{ - } \color{#FF6800}{ 18 } - x \geq 6$
 Move the constant to the right side and change the sign 
$4 x - x \geq 6 \color{#FF6800}{ + } \color{#FF6800}{ 18 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ x } \geq 6 + 18$
 Organize the expression 
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \geq 6 + 18$
$3 x \geq \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 18 }$
 Add $6$ and $18$
$3 x \geq \color{#FF6800}{ 24 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } \geq \color{#FF6800}{ 24 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } \geq \color{#FF6800}{ 8 }$
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Inequality
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