Test 6 calc section number 28

There are two equally valid ways to go here. If you’ve read enough of me, though, you won’t be surprised to learn that I’ll suggest the simpler, less mathy way first.

The question tells you that two points are both 3 units away from –4. You don’t need to make any equations to know what those points are! They’re –1 and –7! So just work through the answer choices until you find one that is true for both x = –1 and x = –7. Start with choice A: Algebraically, what’s happening here is that you’re looking to write an equation for “the positive difference between x and –4 is 3.” The way you write “the positive difference” algebraically when you don’t know which of the values you’re subtracting is bigger is you put the subtraction in absolute value brackets. Therefore, “the positive difference between x and –4″ is written .
The reason I love the simpler way on this question is that you can just as easily write for the positive difference between x and –4. That’s equivalent because of the absolute value brackets, of course, but if that’s what you start out writing, you might not recognize the correct answer choice right away. If, on the other hand, you just start out by finding the answer choice that works for –7 and –1, you can’t go wrong!