Explanation for Question 11 From the Math (No Calc) Section on the Official Sat Practice Test 9
Question 11 gives us this expression and it asks which of the following represents 2 all the possible values of X that satisfy the equation above. 3 So we have this expression right here and 4 the first step to solving is going to be cross multiplication. 5 So we have X times two, two X is equal to X minus 6 three times two X, 7 two X is equal to X times two X, 8 two X squared, negative three times two X is negative six 9 X. Now let's move this X over 10 to the other side. So we have it set up as a, 11 um, a, 12 um, we have zero is equal to something else. 13 So we have two X squared minus six X minus two X. 14 So we have two X squared minus eight X. 15 Now from here, what we can do is we see that both sides are, 16 we see that we can divide both sides by two third divided by two 17 is just zero and we're left with X squared minus four X. 18 Okay. So to find the values of X that satisfy the equation, 19 we're looking to essentially the solution of this equation. 20 And one way to do that is to factor this X squared minus four 21 X into X plus something, 22 or minus something times X plus or minus something is equal to zero. 23 we can tell that one of these is not going to have a 24 number within it. So essentially because there's no constant at the end, 25 like plus four plus 16, plus any other number, 26 we know that we can factor out an X from this expression. 27 So if we take out X, we get X times X is equal to 28 X squared, minus four is equal to four X. 29 So we have zero is equal to X times X minus four. 30 And then to find the solutions to this, this expression is going to be 31 equal to zero. When X minus four is equal to zero, 32 or when X is equal to zero. So we have that. 33 This is true when X equals four, or excuse me, 34 this should say we're an X equals zero. 35 So we have that. This is true when X is equal to four or 36 when X is equal to zero. So those are our two answers for this 37 question. And we can select B as our answer 38 choice.