I think I got the answer for problem 43....does R equal R(-2, 7) ...?
?? of course $\displaystyle x_1$ is not given, that's what we want to find. if at this point you're not able to solve such an equation, you are in trouble
$\displaystyle \frac {x_1 - 4}{2} = -1$
$\displaystyle \Rightarrow x_1 - 4 = -2$ ...............multiplied both sides by 2
$\displaystyle \Rightarrow x_1 = -2 + 4$ ...............added 4 to both sides
$\displaystyle \Rightarrow x_1 = 2$
please look over what i did carefully. i'm in no rush, i'm not expecting you to get it right away, so don't get impatient thinking i'm waiting over you to get it. take your time and read through why i set up those equations as i did.
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
$\displaystyle \frac {x_1 + 2}{2} = -2$
$\displaystyle \Rightarrow x_1 + 2 = -4$ .............multiplied both sides by 2
$\displaystyle \Rightarrow x_1 = -4 - 2$ .............subtracted 2 from both sides
$\displaystyle \Rightarrow x_1 = -6$
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.......
just remember, when you are trying to solve an equation for a variable you are trying to get that variable on one side of the equation by itself. to do this, you must perform the opposite operation of anything operating on the variable, so as to get rid of it.
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
the -12 is wrong