Which correctly compares \( (528 \times 65)-85 \) and \( (528 \times 65)-75 \) without doing any calculations? \( (528 \times 65)-75<(528 \times 65)-85 \) \( (528 \times 65)-85=(528 \times 65)-75 \) \( (528 \times 65)-85>(528 \times 65)-75 \) \( (528 \times 65)-85<(528 \times 65)-75 \)

Let's start with a little numerical deduction! Both expressions \( (528 \times 65)-85 \) and \( (528 \times 65)-75 \) share a common part, \( (528 \times 65) \). The only difference comes from the constants being subtracted. Since subtracting a smaller number (75) results in a larger outcome compared to subtracting a larger number (85), we can clearly say that \( (528 \times 65)-75 \) is greater than \( (528 \times 65)-85 \). So, the correct comparison is: \( (528 \times 65)-85<(528 \times 65)-75 \). Now, let's sprinkle in some related knowledge! Mathematically, when comparing expressions that are identical except for an additive constant, the expression with the smaller constant will always yield a greater result. This is a fundamental property of inequalities, and it helps to simplify many comparisons in algebra. If you're ever perplexed by comparing similar expressions, remember this nifty trick: focus on what’s being added or subtracted. If it’s negative, think larger; for positive constants, think smaller. This way, you can deduce relationships quickly without heavy calculations!