- true or false: If a rumber minus 3 is at most 12 , or 1 more than 2 times the number is at least 25 , then the number must be less than or equal to 15 . or greater thal or equal to 12 .

To tackle this claim, let’s break down the conditions. The first condition states that if we take a number \( x \) and subtract 3, this result must be at most 12. This translates to the inequality \( x - 3 \leq 12 \) or \( x \leq 15 \). The second condition tells us that one more than twice the number must be at least 25, represented as \( 2x + 1 \geq 25 \), leading to \( 2x \geq 24 \) or \( x \geq 12 \). Therefore, \( x \) must be between 12 and 15, making the statement true. Now, let’s illustrate how this connects to real-world decision-making. Imagine you're planning a budget for an event. You have a limit of spending no more than $15 (the first condition) and you also need to ensure there's a minimum of $25 worth of supplies (the second condition). By setting these ranges, you ensure that your spending keeps your event within a financially smart framework, just as we did with the number bounds above! Remember that checking inequalities can sometimes be tricky! A common mistake is misreading the conditions, leading to the wrong conclusion. Always rewrite your inequalities clearly, checking the relationship between the numbers. Additionally, plug in some test values from your determined range to ensure everything holds true. A little verification can prevent making incorrect assumptions in both math and life scenarios!