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Find the solution set (values of X) for the following inequality

|3X - 2| <= |2X - 5|.

Tricky one...did a lot of plugging in numbers.

-3<= x <= 7/5

Lower Limit Plugged in numbers to find the lower limits. Also, realized that when x is neg, both sides of the equation (within the absolute value) are negative. Therefore, we can solve:

2-3x <= 5-2x
-3<= x

Upper Limit Plugged in x = 1 , Worked
Plugged in x = 2, Did not work

So I know the upper limits is between 1 and 2. Looking at the problem, I also know that when x = 1, the right side of the equation is negative and the left side is positive (within the absolute value).

So to find the upper limit I reversed the right side of the equation:
3X - 2 <= 5 - 2X
x <= 7/5

Find the solution set (values of X) for the following inequality

|3X - 2| <= |2X - 5| (*).

Yes, squaring is one method but it's not advisable in case we can't factorize the obtained expression.

My method is breaking the | | by considering ranges of x.
We have two critical values of x which are 2/3 and 5/2
1) x> 5/2
--> (*) <=> 3x-2<=2x-5 --> x<=-3 , but x>=5/2 ---> eliminate this case
2) 2/3<=x<=5/2:
(*) <--> 3x-2<= 5-2x ---> x<=7/5. Check the precondition --> 2/3<=x<=7/5
3) x< 2/3
(*) <--> 2-3x<= 5-2x --> x>=-3. Check the condition--> -3<=x<=2/3