Can abs(28-7w)=7abs(w)
be written as abs(w-4)=abs(w)
and if so why surely it should be
abs(4-w)=abs(w)
can any one explain why I can just chane the signs
Yes, it can be written that way.
I don't see that you have changed any signs, you factored a postive seven out of both sides, and divided it out.
Thanks
To understand why the equation can be written as abs(w-4)=abs(w), let's go through the steps of simplifying the original equation, abs(28-7w)=7abs(w).
1. Start by factoring out a 7 from both sides of the equation:
abs(28-7w) = 7abs(w)
7 * abs(4-w) = 7 * abs(w)
2. Notice that we now have a common factor of 7 on both sides. Divide both sides by 7:
abs(4-w) = abs(w)
At this point, we have simplified the equation to abs(4-w) = abs(w), which can be rewritten as abs(w-4) = abs(w).
The reason you can change the order of subtraction (w-4 to 4-w) without affecting the equation is because the absolute value function only cares about the distance from zero, not the order of the numbers.