MA wrote:

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