Which expression is equivalent to

Which expression is equivalent to

-9+f+2f ?

-8+2f -6f

-8f

-9+3f

The correct answer and explanation is:

The correct expression is -9 + 3f.

Explanation:

When simplifying an algebraic expression, the goal is to combine like terms. Like terms are terms that have the same variable raised to the same power. Here, the only variable is f, so we focus on the terms that contain f.

1. The given expression is -9 + f + 2f.
2. The constant term is -9 (this does not contain the variable f).
3. The terms with the variable f are f and 2f.
4. These two terms can be combined because they are like terms. Specifically, f is equivalent to 1f, so: f+2f=(1f)+(2f)=3ff + 2f = (1f) + (2f) = 3f
5. Now the expression becomes: −9+3f-9 + 3f This is the simplified form of the expression.

The other options:

• -8 + 2f – 6f involves combining like terms on the variable side, but the coefficients do not match what we need. After combining 2f and -6f, we get -4f, which is incorrect.
• -8f is not correct because there’s no way to combine terms that result in a coefficient of -8 for f.

Thus, -9 + 3f is the correct simplified expression.