In an equation, when we change a variable or number sides, we change its sign from positive to negative and vice-versa, right?
So in 738 = a + b, shouldn't it be: -a = -738 + b? Or at least: a = -738 + b as opposed to what chatgpt is telling me
No, you seem to have made a mistake. If you start with (738 = a + b), and you want to isolate (a), you should subtract (b) from both sides, not add it. The correct step would be (a = 738 - b).
The answer visually makes sense... But what about the rule of transposing and changing numbers sign?
I tried solving it online.. 738 = a + b, solving for a, it tells me a = (-738)/(-1) I don't understand...
Quoting another website..
To solve 2x –3 = 13 by transposing, we do the following:
Instead of adding 3 to both sides,we can transpose the 3 that’s already there by
moving it from the left side, over the equal sign, to the right side, and changing its sign from “–” to “+.” Now we have 2x = 13 + 3
I strongly recommend that learners not think of mathematical operations in terms of their cosmetic outcomes (which side of the equation they're on, for example); that just leads to misremembered rules and an inability to understand why rules are valid. Instead, think of the mathematical operations themselves. For example, we are allowed to subtract the same quantity from both sides of an equation.
So if we start from $738=a+b$, we are allowed to subtract $a$ from both sides of the equation, yielding $738-a = a+b-a$ or simply $738-a=b$. From there, subtracting $738$ from both sides of the equation yields $738-a-738=b-738$, or simply $-a=b-738$ (which you correctly found).
ChatGPT's answer is also correct (this time...): subtracting $b$ from both sides of the original equation does yield $738-b=a$. (Wherever $a = (-738)/(-1)$ came from, it's not correct in general.)