Question

5/12-(x-3)/6≤(x-2)/3

Solve with a step by step answer please

Answer 1

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

Answer 2

For this case we must resolve the following inequality:

`\frac {5} {12} - \frac {(x-3)} {6} \leq \frac {(x-2)} {3}`

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:

`\frac {5} {12} - \frac {x} {6} + \frac {3} {6} \leq \frac {x} {3} - \frac {2} {3}`

We add similar terms from the left side:

\
`\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}`

We simplify:

`\frac {11} {12} - \frac {x} {6} \leq \frac {x} {3} - \frac {2} {3}`

Add
`\frac {2} {3}` to both sides of the inequality:

`\frac {11} {12} + \frac {2} {3} - \frac {x} {6} \leq \frac {x} {3}`

Add
`\frac {x} {6}`to both sides of the inequality:

`\frac {11} {12} + \frac {2} {3} \leq \frac {x} {3} + \frac {x} {6}`

We add similar terms to both sides:

`\frac {3 * 11 + 12 * 2} {12 * 3} \leq \frac {6 * x + 3 * x} {18}\\\frac {57} {36} \leq \frac {9x} {18}`

We simplify:

`\frac {19} {12} \leq \frac {x} {2}`

We multiply by 2 on both sides of the inequality:

`2 * \frac {19} {12} \leq x`

We simplify:

`\frac {19} {6} \leq x`

Thus, we have to:

`x \geq \frac {19} {6}`

ANswer:

`x \geq \frac {19} {6}`