The minimum value of $$f(x)=|3-x|+|2+x|+|5-x|$$ is equal to  _____________.

$$f(x)=|3-x|+|2+x|+|5-x|$$

We will check the inflection points, because any set of values less than the least inflection value point, or any values more than the highest inflection point will give a higher value than it's minimum

Inflection Points are = -2, 3, 5

At x = -2 => $$f(x)=|3-(-2)|+|2+(-2)|+|5-(-2)|=12$$

At x = 3 => $$f(x)=|3-3|+|2+3|+|5-3|=7$$

At x = 5 => $$f(x)=|3-5|+|2+5|+|5-5|=9$$

Thus, the minimum value of f(x) = 7, at x = 3.