The problem asks to translate the sentence into an inequality:

"Two times the sum of a number and 21 is at most 26."

We are told to use the variable $b$ for the unknown number. Let's break it down step by step:

• "Two times the sum of a number and 21" can be written as: $2(b + 21)$

• "is at most 26" means that the expression should be less than or equal to 26, represented as: $\leq 26$

Putting it all together, the inequality becomes: $2(b + 21) \leq 26$

This is the correct inequality translation.

Would you like any further details or explanation?

Here are 5 related questions to extend this:

1. How would you solve this inequality for $b$?
2. What would the inequality look like if it was "at least 26" instead?
3. How does this type of problem relate to solving equations?
4. What happens if we change the number 21 to a different value?
5. How do you graph the solution to this inequality on a number line?

Tip: When translating word problems into inequalities, always pay attention to key phrases like "at most," "at least," or "greater/less than." These indicate the inequality symbols to use.