how to work out -9x+17-10x=-21x+23
its 43 duhhhhhhhhhhhhhhhhhhhh
that isn't worked outttttttttttttttttttttttttt!~
It's not worked out - nor is her answer correct. So if someone says, "duhhhhhh," don't feel too badly. She obviously didn't know how to solve the problem either and it might help for her to read this.
The idea with something like this is you want to get "x" by itself. Now, whatever you do to one side of the equal sign, you have to do to the other. Let's pretend we both have the same amount of apples.
Matt's apples, we'll call "M"
Lasha's apples, we'll call "L"
To say we have the same amount, we can say M=L. Right? Ok so far?
Now, if someone came up and gave me 2 apples, we would not have the same amount. M+2 does not equal L. But if someone gave you 2 apples also, then we would have the same amount and we could write it like this.
M+2 = L+2
Why am I saying all this? To get the point across that no matter what you do to one side of the equal sign, you have to do to the other. So, let's begin to look at what you have.
<font color="red">-9x</font> + 17 <font color="red">- 10x</font> = <font color="red">-21x</font> + 23
I put all the "x" values in red because that's where we will start. Start by adding the -9x and the -10x, since they're both on the same side of the equal sign.
-9x-10x = -19x
So now our equation looks like this:
-19x + 17 = -21 x +23
Let's get rid of the -21x on the right side. If you have -21 dollars in your bank account and you add 21 dollars to it, you will have 0 dollars (and, as a result, be richer than I am). But remember, to keep everything equal, we need to do it to both sides. So add 21x to both sides.
21x - 19x = 3x
21x - 21x = 0
So now, it looks like this:
3x+17 = 0 + 23
(Obviously, 0 + 23 = 23)
Now, we still need to get "x" by itself. The next step is to subtract 17 from each side so we have 3x by itself on one side.
2x = 23-17
2x = 6
2x means "two times x." So to get rid of the two, we divide both sides by two since multiplication and division are total arch enemies in the world of algebra ;-)
2x / 2 = 1x (you don't need to write the 1)
6 / 2 = 3
So,
x = 3
Now we can check it by plugging in "3" where "x" is.
(-9 * 3) + 17 - (10*3) = -(21 * 3) + 23
-27 + 17 - 30 = -63 + 23
-40 = -40
Yup. x = 3
....not 43 :)
Matt
I made a mistake above. My apologies. Just a typo.
Here is what I meant to say, with the correction:
It's not worked out - nor is her answer correct. So if someone says, "duhhhhhh," don't feel too badly. She obviously didn't know how to solve the problem either and it might help for her to read this.
The idea with something like this is you want to get "x" by itself. Now, whatever you do to one side of the equal sign, you have to do to the other. Let's pretend we both have the same amount of apples.
Matt's apples, we'll call "M"
Lasha's apples, we'll call "L"
To say we have the same amount, we can say M=L. Right? Ok so far?
Now, if someone came up and gave me 2 apples, we would not have the same amount. M+2 does not equal L. But if someone gave you 2 apples also, then we would have the same amount and we could write it like this.
M+2 = L+2
Why am I saying all this? To get the point across that no matter what you do to one side of the equal sign, you have to do to the other. So, let's begin to look at what you have.
<font color="red">-9x</font> + 17 <font color="red">- 10x</font> = <font color="red">-21x</font> + 23
I put all the "x" values in red because that's where we will start. Start by adding the -9x and the -10x, since they're both on the same side of the equal sign.
-9x-10x = -19x
So now our equation looks like this:
-19x + 17 = -21 x +23
Let's get rid of the -21x on the right side. If you have -21 dollars in your bank account and you add 21 dollars to it, you will have 0 dollars (and, as a result, be richer than I am). But remember, to keep everything equal, we need to do it to both sides. So add 21x to both sides.
21x - 19x = 2x
21x - 21x = 0
So now, it looks like this:
2x+17 = 0 + 23
(Obviously, 0 + 23 = 23)
Now, we still need to get "x" by itself. The next step is to subtract 17 from each side so we have 2x by itself on one side.
2x = 23-17
2x = 6
2x means "two times x." So to get rid of the two, we divide both sides by two since multiplication and division are total arch enemies in the world of algebra ;-)
2x / 2 = 1x (you don't need to write the 1)
6 / 2 = 3
So,
x = 3
Now we can check it by plugging in "3" where "x" is.
(-9 * 3) + 17 - (10*3) = -(21 * 3) + 23
-27 + 17 - 30 = -63 + 23
-40 = -40
Yup. x = 3
....not 43 :)
Matt
To solve the equation -9x + 17 - 10x = -21x + 23:
Step 1: Combine like terms on both sides of the equation.
-9x - 10x + 17 = -21x + 23
Simplifying the left side gives -19x + 17 = -21x + 23.
Step 2: Get rid of -21x on the right side by adding 21x to both sides of the equation.
-19x + 17 + 21x = -21x + 23 + 21x
Simplifying this gives 2x + 17 = 23.
Step 3: Get x by itself on one side by subtracting 17 from both sides of the equation.
2x + 17 - 17 = 23 - 17
Simplifying this gives 2x = 6.
Step 4: Divide both sides of the equation by 2 to solve for x.
2x/2 = 6/2
This simplifies to x = 3.
So, the solution to the equation -9x + 17 - 10x = -21x + 23 is x = 3.