[Video] Q13: The equation 24x^2 +25x - 47 / ax -2 = -8x -3 - 53/ ax-2 is true for all values of x except 2/a, where a is a constant. what is the value of a ?

Explanation for Question 13 From the Math (No Calc) Section on the Official Sat Practice Test 3

Now working on number 13, you've got a pretty big complicating looking equation, 2 right. And we're told that X can't be equal to two over a and 3 a is some constant. Um, 4 and so we're asking ourselves, what is the value of a and so something 5 that will make this, uh, this a lot easier would be since we only 6 have one equation to just have one variable, 7 right? Not two variables. And so we can go ahead and start out by 8 saying that X is equal to one. Let's go ahead and say, 9 X is equal to one and really simplify, 10 um, what is happening here? Right? 11 So we've got 24 times one, which would just be 24 plus 25 times 12 one, which is just 25 minus 47, 13 over a times one, which is just a minus two, 14 we'll set that equal to negative eight minus three, 15 minus 53, over a minus two. 16 So now we can do some simplification, right? 24 plus 25. 17 That's 49 minus 47. 18 So that's two. So we've got two over 80 minus two is equal to 19 eight minus three, that's negative 11 minus 53, 20 over a minus two. 21 And so what we can do here in now is, 22 um, get this a minus two to the, 23 or rather this a minus two, this term, 24 over to the other side of our equation, 25 we can get all the A's together, right? So I'll add 53 over 80 26 minus two, and I'll add 53 over 80 minus two. 27 And when I add that, I now get 55, 28 right? 53 plus two, I have 55 over 80 minus two is equal to 29 negative 11. That negative 11 is over one. 30 Um, and so what I can do now is cross multiply so that...