Let's break down the problem step by step.

Problem Statement

• The sum of two numbers is 26.
• Let x represent the smaller of the two numbers.
• We need to translate the difference between "three more than the larger number and twice the smaller number" into a variable expression and simplify it.

Step 1: Define the numbers

Since the sum of the two numbers is 26, and x represents the smaller number, we can express the larger number as: $\text{Larger number} = 26 - x$

Step 2: Translate the expression

The problem asks for "the difference between three more than the larger number and twice the smaller number."

• Three more than the larger number: $(26 - x) + 3 = 29 - x$
• Twice the smaller number: $2x$
• The difference between them: $(29 - x) - 2x$

Step 3: Simplify the expression

Simplify the difference: $29 - x - 2x = 29 - 3x$

Final Expression

The simplified expression for "the difference between three more than the larger number and twice the smaller number" is: $29 - 3x$

Would you like further details on this, or do you have any questions?

Here are some related questions you can explore:

1. How would the expression change if the sum of the two numbers was different?
2. What happens to the expression if instead of three more, it's five more than the larger number?
3. How can you express twice the larger number minus the smaller number?
4. What would the expression be if you were given three less than the larger number?
5. How does changing the operation (e.g., sum instead of difference) affect the expression?

Tip:

When translating word problems into algebraic expressions, carefully identify the operations (sum, difference, product) and keep track of what each variable represents.