Explanation for Question 5 From the Math (No Calc) Section on the 2020 October Sat
So question number five is asking us for the function H as defined above, 2 what is the value of X when H of X is equal to negative 3 two? So here, what we're solving for is the X. 4 And what we're given is H of X. 5 So we can rewrite the equation that they gave us adding in the new 6 information that they told us in the question. And the first thing that they 7 told us was the H of X is negative two. 8 So I'll start by replacing H of X with negative two, 9 and then just rewriting the equation. Same as before. 10 It's important to note that you can't put negative to where the X's, 11 because we don't know what X is. That's what we're solving for. 12 What we know is the H of X is negative two. And then from 13 here we just solve for X. Like we normally would. 14 First thing we can do is distribute, right? First thing you always want to 15 do when you solve for X is get rid of any parentheses by distribution. 16 So we have negative two is equal to negative four X plus four plus 17 two. Now we can kind of combine like terms on the right side here. 18 We've got negative. Two is equal to negative four X and then four plus 19 two is six. So we can rewrite that, 20 replacing it with a six. And now our next goal is going to be 21 to get all the normal numbers to one side of the equation and all 22 the X's to the other. And so I can do that by moving this 23 positive six over here and subtracting six from both sides that 24 tells me that negative eight is equal to negative four X, 25 six is canceled. And the last thing I need to do is divide by 26 negative four so I can get X on its own. Now I have two 27 is equal to X and our correct answer will be de.