WholeLottaLove wrote:
Haha - I am lost (not your fault...I am just very slow with mathematical concepts, unfortunately)
I understand that for certain values of x,(say if x =2) (4x-1) and (x+1) would be positive but (x-3) would be negative. But why would we bother finding what is positive and what is negative? I almost feel as if testing a series of integers and fractions, both positive and negative, would be a quicker way to figure out the right answer. Still, I am trying to get the concepts buttoned down.
What I explained above is how to study an abs value from a theoretical point of view, because you original methos is wrong.
Of course this is not required to answer the question, you can try with real number and see what you find out.
But am I trying to explain how an abs function works, for instance your original method
I. f(x) = (4x-1) + (x-3) + (x+1)
II. f(x) = -(4x-1) + -(x-3) + -(x-1)
does not work to find the answer. The function cannot be reduced to that form!
"But why would we bother finding what is positive and what is negative? "
This is required to study an abs value. In my original post you see the graph of F(X), and you notice that is defined into sections.
Each section is one of the intervals above, and in each one of those the fucntion has a different equation.
The concept that I apply here is the same as the one that you would apply to solve
\(y=|x|\)
How would you study this?
for x>0 => y=x
for x<0 => y=-x
Define where the funct is positive, treat each part as a separate equation. The concept in the question is the same, only involves more intervals.