Answer:x>3 1/6
Step-by-step explanation:
5/12-(x-3)/6 <(x-2)/3
5/12 *12-(x-3)/6*12<(x-2)/6*12
5-2(x-3)<4(x-2)
5-2x+6<4x-8
-2x+11<4x-8
-2x<4x-19
-6x<-19
-6x(-1)<-19(-1)
6x>19
x>19/6
x>3 1/6
just change all the inequality signs to a x is greater or equal to 3 1/6 and on the rest change to and < and equal sign only put > or equal sign on the last three lines
For this case we must resolve the following inequality:
[tex]\frac {5} {12} - \frac {(x-3)} {6} \leq \frac {(x-2)} {3}[/tex]
We apply distributive property to the terms within the parenthesis of the left side of the inequality and separate the terms from the right side:
[tex]\frac {5} {12} - \frac {x} {6} + \frac {3} {6} \leq \frac {x} {3} - \frac {2} {3}[/tex]
We add similar terms from the left side:
\[tex]\frac {5} {12} + \frac {3} {6} - \frac {x} {6} \leq \frac {x} {3} - \frac {2} {3}\\\frac {5} {12} + \frac {1} {2} - \frac {x} {6} \leq \frac {x} {3} - \frac {2} {3}\\\frac {2 * 5 + 12 * 1} {12 * 2} - \frac {x} {6} \leq \frac {x} {3} - \frac {2} {3}\\\frac {22} {24} - \frac {x} {6} \leq \frac {x} {3} - \frac {2} {3}[/tex]
We simplify:
[tex]\frac {11} {12} - \frac {x} {6} \leq \frac {x} {3} - \frac {2} {3}[/tex]
Add[tex]\frac {2} {3}[/tex] to both sides of the inequality:
[tex]\frac {11} {12} + \frac {2} {3} - \frac {x} {6} \leq \frac {x} {3}[/tex]
Add [tex]\frac {x} {6}[/tex]to both sides of the inequality:
[tex]\frac {11} {12} + \frac {2} {3} \leq \frac {x} {3} + \frac {x} {6}[/tex]
We add similar terms to both sides:
[tex]\frac {3 * 11 + 12 * 2} {12 * 3} \leq \frac {6 * x + 3 * x} {18}\\\frac {57} {36} \leq \frac {9x} {18}[/tex]
We simplify:
[tex]\frac {19} {12} \leq \frac {x} {2}[/tex]
We multiply by 2 on both sides of the inequality:
[tex]2 * \frac {19} {12} \leq x[/tex]
We simplify:
[tex]\frac {19} {6} \leq x[/tex]
Thus, we have to:
[tex]x \geq \frac {19} {6}[/tex]
ANswer:
[tex]x \geq \frac {19} {6}[/tex]
