Question

Which of the following represents the solution of x - 8 < -2 in set notation?

The answer that I got was
x <-10

Answer 1

I'm afraid not Isabella. Remember, you're pretending that you have an equation here, so everything you do to one side, you do exactly the same to the other side. You started with\[x-8 <-2\], and you correctly took the step of adding 8 to the left, so you have to do the same to the right:\[x-8\textbf{+8} < -2\textbf{+8}\]

Answer 2

I am confused?

Answer 3

You started with \[x-8<-2\]Imagine that's like a scales that's perfectly balanced. You have some amount x-8 on one side of the scales, and you have -2 on the other side of the scales.
Now you need to get just x on the left side, and just a number on the right side. To do that, you need to add 8 to the left side, because \(x-8+8=x\). But wait! You added something to the left side of the scales, but didn't do anything to the right side of the scales, so it's not balanced anymore. To balance it, you need to add 8 to the right side of the scales, i.e. \(-2+8\). So you get:\[x-8\textbf{+8} < -2\textbf{+8}\]\[x<6\]