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Formula
Solve the inequality
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$- \dfrac { 1 } { 2 } x + 3 \geq 1$
$- \dfrac { 1 } { 2 } x + 3 \geq 1$
Solution of inequality
$x \leq 4$
$- \dfrac{ 1 }{ 2 } x+3 \geq 1$
$x \leq 4$
 Solve a solution to $x$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } + 3 \geq 1$
 Calculate the multiplication expression 
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 2 } } + 3 \geq 1$
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { x } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \geq \color{#FF6800}{ 1 }$
 Multiply both sides by the least common multiple for the denominators to eliminate the fraction 
$\color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \geq \color{#FF6800}{ 2 }$
$- x \color{#FF6800}{ + } \color{#FF6800}{ 6 } \geq 2$
 Move the constant to the right side and change the sign 
$- x \geq 2 \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
$- x \geq \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 6 }$
 Subtract $6$ from $2$
$- x \geq \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } \geq \color{#FF6800}{ - } \color{#FF6800}{ 4 }$
 Change the symbol of the inequality of both sides, and reverse the symbol of the inequality to the opposite direction 
$\color{#FF6800}{ x } \leq \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right )$
$x \leq \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 4 \right )$
 Simplify Minus 
$x \leq 4$
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