[Video] Q8: X + 1 = 2/x + 1 in the equation above, which of the following is a possible value of x + 1 ?

Explanation for Question 8 From the Math (Calc) Section on the Official Sat Practice Test 8

So question number eight, asks us for possible value of X plus one, 2 and a possible reason why this question might be difficult is because normally students 3 are used to being asked for what the value of Xs. 4 Right. But here they've asked us for X plus one. 5 And so you might be a little confused about how you solve for this 6 whole set rather than just one variable. 7 Right? And so there's a couple of ways you could think about doing this. 8 You could still just solve for X and then add one to it. 9 Or perhaps it is easy to just solve for X plus one as a 10 whole. So we'll see, as we go through this problem, 11 what the best way to actually go about this is, 12 so if we rewrite this here, we see that we have a denominator, 13 right? We have a denominator right here. 14 And so the best thing to do is going to be, to get rid 15 of that denominator by multiplying both sides by X plus one, 16 that'll remove this denominator here, but that'll create this side. 17 We can write it as X plus one squared. And so that's, 18 it's true that you could foil it out and you could get something that 19 looks a little bit more like X squared, plus two X plus one. 20 But we'll see in a second, why it's easier to actually write it is 21 X plus one squared and that'll be equal to two. 22 And now we can see that if I want to find X plus one, 23 all I have to do is square root, 24 both sides, right? Because the square root of X plus one squared is just 25 X plus one, and that'll be equal to the square root 26 of two positive or negative. 27 Right? And if we look at our answers, we see that the square root 28 of two positive is one of our answer choices. 29 So our best answer is going to be, be the square root of two.