In your PWN Math Book Fourth Edition on page 87 question 5, I do not understand why 6.5 changed to negative 6.5 when you took the absolute value of both sides. Wouldn’t it stay 6.5?
Here’s the question:
What the solution in the back of the book is saying is that once you isolate the absolute value:
…you need to recognize that could equal either or . You’re not taking the absolute value of both sides there, you’re recognizing that an absolute value is already being taken on the left, so of course the right is positive. If there were no absolute value on the left, the right could be positive or negative.
So look at both possibilities!
Since the question asks for the minimum value of , you want .
What the solution is doing is just recognizing that the smaller value will come from the scenario and therefore only showing that calculation.
Does that help?