SOLUTION: here is the problem 1 is less than or equal to -w/2 My question is in the answer the variable is switched to the other side. I am asking why?

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Question 102694: here is the problem 1 is less than or equal to -w/2
My question is in the answer the variable is switched to the
other side.
I am asking why?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given inequality

Multiply both sides by 2

Multiply both sides by -1 to isolate w (note: Remember, multiplying both sides by a negative number flips the inequality sign)

Now since we're reading from left to right, what does this symbolic inequality say in English? Well it says that -2 is greater than or equal to w. However, many might read this as: w is greater than or equal to -2 (since most would see the greater than sign and connect that with the "w") and make a false conclusion. In other words, they would see the w and the greater than sign together and think that w is greater than when in fact it's not.

So to make things simple, everything is flipped (even the sign) to get

Which in plain English reads: w is less than or equal to -2

So which of the two is easier to read?

So in a sense, it's all about how you perceive the answer. The first solution is perfectly fine. But since many may translate the solution wrong, it is better to use the second method.