I think I got the answer for problem 43....does R equal R(-2, 7) ...?
as for the equations you have, they are correct, i have no idea how you got your answers.
but think... if x_1 was -2, then x_1 + 2 would be zero, right? and zero divided by 2 is zero, right? and we are all aware that zero is not equal to -2.
Let's go through the equation with x_1
.............multiplied both sides by 2
.............subtracted 2 from both sides
now, let's think of it another way. these equations are simple enough to navigate through with common sense.
i have a number, when i divide it by 2 i get -2. what must that number be? well, 4 divided by 2 is 2, so i guess the number has to be -4 to get -2. ok, so i have x_1 + 2 being divided by 2 gives -2, so x_1 + 2 must be -4. what does x_1 have to be, so that when i add 2 to it i get -4? well, -6 of course. 2 - 6 = -4, which is what i want. thus, x_1 = -6
i seriously recommend brushing up on basic algebra. you will have a really hard time with this class if you don't
Uh...yes, I definitely need to brush up my basic algebra skills. I haven't done algebra since last May so I'm very rusty as you can see.
As for basic algebra skills, I'm still having trouble understanding how to keep the x_1 alone or more so, multiple x_1 times 2.......
if i have x + 2 = 5
i want to solve for x (meaning, i want to have x by itself). how do i do that? well, i have to get rid of the 2. how do i get rid of 2? i subtract it. that's it, i can take it away. so i apply the opposite operation of -2 to the operation +2 and i get rid of the 2. so i get:
x + 2 - 2 = 5 - 2
=> x = 3
of course, you realize a minus 2 appears on the right. that's because we are in an equation, to keep things balanced, whatever i do on the left i must do on the right, and vice versa.
if i have x/2 = 10
same story. i have a division by 2 working on the x. to get x by itself, i must multiply by 2, which is the opposite operation to cancel out the current one. and since i'm in an equation, i must multiply the other side by 2 as well. so i get:
(x/2)*2 = 10*2
=> x = 20