Question

Which expression correctly represents “six more than the product of five and a number, decreased by one”?
6 + 5 n minus 1
6 + 5 + n minus 1
6 + 5 (n minus 1)
(6 + 5) n minus 1

Answer 1

To break down the expression "six more than the product of five and a number, decreased by one," we can analyze it step-by-step:

1. "the product of five and a number": This can be represented as \( 5n \), where \( n \) is the number.

2. "six more than the product": This means we add 6 to the product, giving us \( 5n + 6 \).

3. "decreased by one": This indicates we subtract 1 from the result of step 2. So we have \( (5n + 6) - 1 \).

Combining these steps, we arrive at the expression:

\[
5n + 6 - 1 = 5n + 5
\]

Now, let's compare this with the given options:

1. \( 6 + 5n - 1 \): This simplifies to \( 5n + 5 \) (which is correct).
2. \( 6 + 5 + n - 1 \): This simplifies to \( 5 + n + 5 = n + 10 \) (not correct).
3. \( 6 + 5(n - 1) \): This expands to \( 6 + 5n - 5 = 5n + 1 \) (not correct).
4. \( (6 + 5)n - 1 \): This simplifies to \( 11n - 1 \) (not correct).

Therefore, the correct expression is:

**\( 6 + 5n - 1 \)**.