Write an algebraic expression that models the word phrase.

the product of 

22 

and the sum of a number x and 19

The word phrase describes the product of two quantities: "22" and "the sum of a number \(x\) and 19."

To write this as an algebraic expression:

1. **Sum of a number \(x\) and 19**: This can be written as \(x + 19\).
2. **Product of 22 and the sum**: This is written as \(22(x + 19)\).

So, the algebraic expression is:
\[
22(x + 19)
\]

Would you like further details or have any questions?

Here are some related questions:

1. How would you distribute the 22 across the expression \(22(x + 19)\)?
2. What happens if you change "sum" to "difference" in a word problem?
3. How do you handle similar expressions with division instead of multiplication?
4. How would this expression change if the word phrase involved "the product of 22 and the difference between a number \(x\) and 19"?
5. Can you explain how to combine like terms in an expression after distribution?

**Tip:** When translating word phrases into algebraic expressions, always identify the operations described (sum, product, difference, etc.) and apply them correctly.

Learn how to model the algebraic expression for the product of 22 and the sum of a number x and 19. This problem covers basic algebraic operations and expression modeling suitable for Grades 7-9 students.

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