A lift has a maximum load of (500) kilograms. If the total load is (w), which inequality is correct?

Correct answer: (w\le500)

The direct answer is A: \(w\le500\). The phrase maximum load of 500 kg means the lift may carry 500 kg or any smaller non-negative load. “Maximum” includes the limiting value, so the correct symbol is \(\le\), read as less than or equal to. Option A correctly allows w=500 as well as smaller values. Option B, \(w<500\), wrongly excludes exactly 500 kg; it would describe a strict limit below 500. Option C, \(w\ge500\), says the load must be at least 500 kg, which is not the meaning of a maximum and would allow heavier loads. Option D, \(w>500\), says the load must exceed the safe limit and is clearly unsafe. Physically, w cannot be negative, but that extra fact is not needed among the options. Memory cue: maximum means “at most,” so use \(\le\); minimum means “at least,” so use \(\ge\).