I solved the following two Algebra problems (with proof) but everyone seems to think its Incorrect. Is it?

Question

PROBLEM # A: 1 = -2-(4-W)
W = -2-1-(4)
W = -2-1-4
W = -7
This is how I proved it:
1 = -2-(4-7)
1 = -2-(-3)
1 = -2+3
1 = 1

Here is the next one
PROBLEM B: 4-(1+X) = 5
4-1-X = 5
-X = 5-4+1
-X = 1+1
-X = 2
X = -2
This is how I proved it:
4-{(1+(-2)} = 5
4 - (1-2) = 5
4 - (-1) = 5
4 + 1 = 5
5 = 5

Please answer in following manner :
PROBLEM # A: Correct or Incorrect and Why?
PROBLEM # B: Correct or Incorrect and Why?

Also has anyone ever solved an Algebra problem quite this way?

(No Assumption Please!!!) Thanks for your time.

Answer 1

I did your math wrong on problem A. To solve for W, you need to get W by itself on one side of the equals sign. So you need to simplify first: 1=-2-(4-W) = 1=-2-4+W
Now solve:1=-2-4+w
1+2+4=W
7=W
Problem B is correct, because you did the math right. If you want to get a -3 to the other side of an equals sign, you must add it (+3) to cancel it out on one side, and since you must do on one side what you do on the other, it adds itself to the other side, the one you want

Answer 2

Problem A is wrong!

Here's the step:

1= -2-(4-w)
1= -2 -4 + w ( you have to multiply the -1 to 4 and -w )
1= -6 + w ( you subtract -2 and -4 together you get -6 )
1 +6 = -6 +6 + w ( you have to add 6 on both side to get rid of -6 on the right side of the equation )
7= w

Check to make sure correct!

Step:

1= -2 -(4-w)
1 = -2 -(4-7) substitute w for 7 because that's what the value of w )
1= -2 -4 + 7 that's what you get when you multiply -1 to 4 and - 7
1= -6 + 7 add -2 and -4 together
1= 1 the equations equal so that means your answer ( 7) was correct!


Problem B was right!

Answer 3

PROBLEM # A: 1 = -2-(4-W)

Simplify to:

1=-2-4+W (the W is a double negative which is a positive!
W=1+2+4
W=7

Prove:

1=-2-(4-7) (if the correct answer was -7, it would be 1=-2-{4-(-7)}!
1=-2-4+7
1=1

You had the answer as -7 but if you took 4-(-7) you would get 11, not -3 as you have it!


PROBLEM B is right.

Answer 4

Problem A is incorrectly solved. W = 7 is correct and not -7.
Your verification is also incorrect. Your answer is W = -7, but in verification, you have put W = 7.

To solve, proceed systematically by first simplifying each side opening the bracket as under.

1 = -2 - 4 -(-W)
1 = -2 -4 + W (minus*minus makes it plus)
1 = -6 + W
7 = W

Problem B is correct.

Answer 5

A: Incorrect. W=7, not -7. When you went to check your answer, you forgot to account properly for the sign of W. Correctly substituting W=-7 would have revealed -2 - (4-(-7)) = -2 - (4+7) = -2 - 11 = -13 ≠ 1.

B: Correct.

Edit: changed wording on the first part of A to make it more polite. The first version sounded like I was insulting you, which wasn't my intent.

Answer 6

A) incorrect
The first line of your proof must be:
1=-2-(4-(-7))
You have plugged in 7 instead of -7 for w.
7 is the right answer, but your previous steps show w=-7.
B) OK

Answer 7

letter a is the only error.
correct solution:
1 = -2-(4-W) --given--
1 = -2-4+W --the negative sign is distributed to 4 and W--
W=1+2+4 --transpose to combine like terms--
W=7

Answer 8

-2 - 4 = -6
You changed the - 4 to + 4 in your solution, why is that?

Same with the second one, you disregarded the - in front of the 1 it is NEGATIVE 1 not POSITIVE 1
negative and negative = more negative