Explanation for Question 17 From the Math (No Calc) Section on the 2019 October Sat
Now in question number 17, we're given this equation here and we're told that 2 w is equal to two. So a good first step, 3 if we want to solve for Z is going to be to rewrite the 4 equation where instead of writing w we actually write to in its place. 5 So you have two Z times two squared, 6 minus three times two minus 10 is equal to two Z. 7 And now we can do a little bit of simplifying to condense this equation, 8 right? Because two squared, we know that's four, 9 right? In two times four, that's eight. So what we really have here is 10 an eight Z and our negative three times two that makes 11 this a negative six and negative six minus 10 is 12 negative 16. So what we have here is rather a, 13 an eight Z minus 16, 14 and that's equal to two Z. 15 So now, if I want to solve for Z, I need to get all 16 disease to one side of the equal sign and all the normal numbers to 17 the other side of the equal side. 18 And in order to do that, I can subtract eight Z from both sides. 19 That way all my Z's on the left cancel out and I'm left with 20 negative 16 is equal to negative six Z. 21 Now, finally, the last thing that's in my way from solving per Z is 22 that negative six. So what I can do is divide by negative six. 23 So these negative sixes will cancel and that'll leave me with 16. 24 Over six is equal to Z, 25 and it's positive because I have a negative divided by a negative, 26 and those negatives are going to cancel. And finally, 27 I just have to simplify the 16 over six. 28 I can divide both 16 and six by two, 29 which leaves me with eight, over three is equal to Z. 30 And so the best answer for number 17 is going to be eight 31 over three.