Explanation for Question 10 From the Math (No Calc) Section on the Official Sat Practice Test 9
Question 10 reads the equation above is true for all X where a and 2 B are Constance. What is the value of a B? 3 So going through this problem, if the equation above is true for all 4 X, that means that no matter what X value you plug in on the 5 left side, you will get the same thing. 6 If you plug the same X value into the right side. 7 So if you think of it as if the left side and the right 8 side are both lines, they're essentially the same line, 9 meaning that they'll have the same slope and same Y intercept having an infinite 10 number of solutions, perfect creation abroad. 11 It's true for all X let's start by writing out the left side of 12 the equation and distributing it appropriately so that it looks more like the right 13 side. So we have X plus three times five X squared, 14 minus BX, plus four, 15 multiply out X times five X squared. 16 We get five, a X squared. 17 Then we have a X times negative BX to 18 get minus a B X squared. 19 Then we have a X times four. 20 So we get plus four, a X, 21 and actually, excuse me, let me make a slight correction here for this first 22 term. Since it's X times five X squared, 23 it should actually be five, eight X cubed. 24 Alright, now let's multiply out the second set of terms. 25 So we have three times five X squared is equal to 15 X squared, 26 and then we have three times 27 negative BX. So we have minus three B X, 28 and then we have three times four. 29 So that's plus 12. And then we have that whole term 30 is equal to...