Final answer:
Nancy has x coins, and Bill has 2x - 6 coins. The total number of coins they both have is the sum of these amounts, which simplifies to 3x - 6.
Step-by-step explanation:
Lets start by expressing the number of coins Nancy and Bill have using algebraic expressions. Nancy has x coins. Bill has 6 coins fewer than twice the number of coins Nancy has, so we can express the number of coins Bill has as 2x - 6.
The total number of coins they have together is the sum of Nancy's coins and Bill's coins. Thus, the expression for the total number of coins is:
x + (2x - 6) = 3x - 6
To simplify the expression, we combine like terms, which in this case are the terms with x. Because there is nothing else to simplify, the simplified expression for the total number of coins Nancy and Bill have together is 3x - 6.