Explanation for Question 8 From the Math (No Calc) Section on the 2017 October Sat
Question eight says in the equation above a is a constant, 2 if no value of X satisfies the equation, 3 what is the value of a so first I'm just going to rewrite this, 4 distributing the terms on the right side of the equation, 5 and that becomes three X plus 15 plus five 6 X plus negative five. And we can add and subtract like terms 7 on the right side to get eight X plus 8 10, and that's equal to two eight X minus 15. 9 Next we can add 15 to both sides to get to AIX is equal 10 to X plus 25 and subtract eight X from both sides. 11 So two, a X minus eight X is equal to 12 25. Now both to AIX and negative eight X have an extra 13 in them. So I'm going to factor that out and rewrite this as two 14 eight minus eight times X is equal to 25. 15 And finally, I'm going to divide 25 by two, 16 eight minus eight, to get that X is equal to 25 over to 17 a minus C. Now the only way that no value of X 18 satisfies this equation is if this, 19 uh, if X is undefined. 20 And that would mean that the denominator of 25 divided by two eight minus 21 eight is equal to zero. That's what makes a F uh, 22 something undefined. So the answer to this can be found 23 by setting to a minus eight equals zero. 24 If we add it to both sides, we get two a is equal to 25 eight. And if we divide both sides by two, 26 we get a, is equal to four, 27 which means that when a is equal to four, 28 no value of X satisfies the equation. 29 So C is the correct damn.