what is the mistake in this question?

Question

Step 1......Let a + b = c + d

Step 2......4 (a + b) = 4 (c +d)

Step 3......3a + a + 3b + b = 3c + c + 3d + d

Step 4......3a + 3b - 3c - 3d = c + d - a - b

Step 5......3 (a + b - c - d) = -1 (a + b - c - d)

Step 6.
.....(a + b - c - d)
.... ---------------- = -3
... (a + b - c -d)

Step 7......3 = -1 or -3 = 1

So........... Find out in which step there is a mistake.?

Answer 1

Step 6 - you're not allowed to divide by 0 (= a + b - c - d)

Answer 2

The mistake is that if we assume that a + b = c + d, then in Step 5, (a + b - c - d) is equal to 0 since (a +b - c - d) = (a + b) - (c + d).

This means that in Step 6, you are dividing both sides of the equation by 0 which is not allowed. This is the Step where the actual mistake is made.

Answer 3

Actually the equation reaches a conclusion at step 5:

Step 5......3 (a + b - c - d) = -1 (a + b - c - d)

3[(a+b)-(c+d)] = -1 [(a+b)-(c+d)]
3* 0 = -1*0

0 = 0
Which is correct.

So, as others have also put it, Step 6 is not allowed. What you are effectively doing is:
3[(a+b)-(c+d)] = -1 [(a+b)-(c+d)]

3 = -1 {[(a+b)-(c+d)] / [(a+b)-(c+d)] }
3 = -1 { 0/0}
Which leads to the erroneous results

Answer 4

step 5 leading to step 6 bring wrong because u divided by 0

Answer 5

step 5 ==>6

"Step 5......3 (a + b - c - d) = -1 (a + b - c - d)

Step 6.
.....(a + b - c - d)
.... ---------------- = -3 "
... (a + b - c -d)

3(a + b - c - d) + 1(a + b - c - d) = 0

Answer 6

step 6, since you cannot divide by 0 .

Answer 7

there are a lot of mistakes. why does step 2 have a 4, and step 3 goes to 3a. when you multiply 4(a+b) it equals 4a+4b.

Answer 8

Step 5:

3(a+b-c-d)= -1(a+b-c-d)

Step6:
3(a+b-c-d)/(a+b-c-d) = -1



Step7:
(a+b-c-d)/(a+b-c-d) = -1/ 3


Step8:

1=-1/ 3

Step 9: 3= -1 or -3 = 1

Answer 9

step 6 is the mistake,
you divide by 0= a + b - c -d

which is a no-no.....

Answer 10

(a + b - c -d) equals zero. Division by zero in step 6 is undefined.