To use the strategy or not?

[user3195]

Here, if we use the manipulating both sides QC strategy, we get quantity A as (x+1) and quantity B as (x-1).

When we compare them after using this strategy A is obviously bigger. But if we don’t use this strategy an do not cancel the x on both sides we can see that when x=0 both sides would be equal.

How to navigate through such problems? Here using the strategy is actually making my life simpler but giving me a wrong answer.

Can anyone help me out please?

[cylverixxx]

When dividing both sides by x - 1, you don’t know whether x - 1 > 0 or x - 1 < 0. You can imagine obtaining a different answer for each case.