Question 102694
{{{1<=-w/2}}} Start with the given inequality



{{{2<=-w}}} Multiply both sides by 2




{{{-2>=w}}} 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 


{{{w<=-2}}}



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 {{{-2>=w}}} is perfectly fine. But since many may translate the solution wrong, it is better to use the second method.