Came across this question just now. Had a hard time trying to
solve it. Do take a look and see where you are able to help.
Sketch the graph of y - 3 = -|3 - 2x| for
-1< or equal to x < or equal to 4. Hence state the
values of x for which y>2
Can't you multiply the - sign into |3-2x| and get |2x-3|? I
understand that this would result in a different answer towards the
end.
But how do you explain this if you were to use this method ( A
correct way) to solve this question?
If f(x) = |x-2| + |4-2x|, show that f(x) = k|x-2|, where k is a
constant to be determined.
so you do something like this : |x-2| + |-2||x-2| = 3|x-2|
Going back to my earlier question, why is it that you can't
mutiply the -1 inside the term but you can factorise it out?
Because |3-2x| = |2x-3|, but both are not equal to -|3-2x| or
-|2x-3|.
|4-2x| = |-2||x-2| = 2|x-2| (because |-2| = 2). Hence that
statement is possible.
Whatever is already inside the modulus you can make it negative
and it'll give you the same positive result, but making what is
outside negative will not satisfy the equation anymore.
