SOLUTION: Respected Sir, My Question is : If |x − 2| + |x − 3| = 7 then x Please Explain me the Doubt clearly in detail ?

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Question 708722: Respected Sir,
My Question is :
If |x − 2| + |x − 3| = 7 then x
Please Explain me the Doubt clearly in detail ?
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
FOUR conditions to check for this equation.

Both expression negative:
2-x%2B3-x=7 (Do you notice I took the OPPOSITE both expressions there?)
-2x%2B5=7
.
x=-1

The Condition that x-2%3C0 and x-3%3E=0:
2-x%2Bx-3=7
2-3=7
FALSE STATEMENT.

The condition that x-2%3E=0 and x-3%3C0:
x-2%2B3-x=7
-2%2B3=7
FALSE STATEMENT.

Both expressions positive:
x-2%2Bx-3=7
2x-5=7
x=6

The occurrance of the false statements is the result of those sets of conditions not being possible
Solution: x=-1 OR x=6

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The two solutions are highlight%28x=6%29 and highlight%28x=-1%29

For 2%3C=x%3C=3, x-2%3E=0 and x-3%3C=0 , then
abs%28x-2%29%2Babs%28x-3%29=%28x-2%29-%28x-3%29=x-2-x%2B3=1
The expression abs%28x-2%29%2Babs%28x-3%29 cannot equal 7%7D%7D%0D%0Aand+we+do+not+find+a+solution+in+the+interval+where+%7B%7B%7B2%3C=x%3C=3
So either x%3E3 , making x-2 and x-3 both positive adding to 7
or x%3C2, making x-2 and x-3 both negative,
adding to -7

Forx%3E3 :
abs%28x-2%29%2Babs%28x-3%29=%28x-2%29%2B%28x-3%29=x-2%2Bx-3=2x-5
We solve 2x-5=7
2x-5=7 --> 2x=7%2B5 --> 2x=12 --> x=12%2F2 --> highlight%28x=6%29

Forx%3C2 :
abs%28x-2%29%2Babs%28x-3%29=-%28x-2%29-%28x-3%29=-x%2B2%2Bx%2B3=-2x%2B5
So -2x%2B5=7 <--> 2x-5=-7
We solve 2x-5=-7
2x-5=-7 --> 2x=-7%2B5 --> 2x=-2 --> x=-2%2F2 --> highlight%28x=-1%29