Answer Choices
{−1}
{5}
{−1, 5}
{0, −1, 5}
Explanation for Question 7 From the Math (No Calc) Section on the Official Sat Practice Test 8
So question seven gives us a nice little equation here and then asks us, 2 what is the solution set to this equation? 3 When it's asking for the solution set, it's just asking us to solve for 4 X. And so kind of as a general rule of thumb, 5 if you read a question and you're not quite sure what it's solving for, 6 looking at your question and see if there's a variable in the equation, 7 odds are you're solving for that variable, 8 right? And here we have an X, so we're going to solve for X. 9 So we can start by writing this out X plus three. 10 And so the first thing that we can do, right, is realize that this 11 four and this three can be condensed together. 12 So let's start there. I'll subtract four from both sides. 13 And I get square root of two X plus six is equal to X 14 minus one. 15 And so now this is what's getting in our way, 16 right? Because it's really hard to solve for X. If we have that radical. 17 And since this is a square root, I can fix this problem by squaring, 18 both sides of my equation. Now, 19 if I square the left side, I get the, this square root is canceled 20 out by the squared and I get two X plus six. 21 Now, if I square the right side, you might be tempted to just write 22 X minus X squared minus one squared. 23 Right? But that's not gonna work because I'm doing X minus one squared. 24 I'm really doing X minus one times X minus one. 25 And I need to foil these out. So X times X is X squared, 26 X minus one is negative X, X minus one is also neg...