understanding conditional equations..

[bobisaka]

To find the solution for the following, I did:

8+3 (4/3 - 4) = 0
8+12/3 - 4 = 0
8+4-4 = 0
8=0

How did the value of a = 4/3 ? Why do I get a contradiction of 8=0?

 

[bobisaka]

8 + 12/3 - 12 =0
8+4-12=0
12-12=0
0=0

Okay i see.

 

[Dr.Peterson]

View attachment 25427


To find the solution for the following, I did:

8+3 (4/3 - 4) = 0
8+12/3 - 4 = 0
8+4-4 = 0
8=0

How did the value of a = 4/3 ? Why do I get a contradiction of 8=0?

I think you're saying, not that you find the solution this way, but that you are checking it, which is a good thing to do.

8 + 12/3 - 12 =0
8+4-12=0
12-12=0
0=0

Okay i see.

So you caught your own error, which was forgetting to distribute. Good.

This is a good lesson: Sometimes a check fails, not because the solution was wrong, but because of a mistake in the check. I often tell students, when the check fails, check the check before giving up on the solution. And the check is good practice in careful evaluation!