Final answer:
The verbal statement 'three times a number increased by 8 is at most 40 more than the number' is expressed as the inequality 3x + 8 ≤ x + 40 in mathematical terms. This inequality simplifies to x ≤ 16, indicating that the original number must be 16 or less.
Step-by-step explanation:
The question involves translating a verbal statement into a mathematical inequality. The phrase 'three times a number increased by 8 is at most 40 more than the number' can be represented algebraically. Begin by letting the variable 'x' represent the unknown number. The phrase 'three times a number' translates to '3x', 'increased by 8' means we add 8, and 'is at most' indicates that the expression is less than or equal to something. '40 more than the number' is translated to 'x + 40'. Combining these elements, we have the inequality 3x + 8 ≤ x + 40.
To solve this inequality, we would subtract 'x' from both sides to get 2x + 8 ≤ 40, and then subtract 8 from both sides to find 2x ≤ 32. Next, we would divide both sides by 2 to get x ≤ 16. This tells us that the original number must be 16 or any number less than 16 to satisfy the condition described in the question.
Understanding how to translate verbal statements into mathematical expressions and inequalities is a fundamental math skill. Knowing terms such as 'at most' is crucial for setting up the correct inequality. This situation is an application of basic algebra to interpret and solve problems.