Question

Ella simplifies (3 b + 4 r) + (negative 2 b minus r) and says the result is b Plus 5r. What error did Ella make?
Ella incorrectly combined the b coefficients. The correctly simplified expression is 5 b + 5 r.
Ella incorrectly combined the b coefficients. The correctly simplified expression is Negative b + 5 r.
Ella incorrectly combined the r coefficients. The correctly simplified expression is b – 5r.
Ella incorrectly combined the r coefficients. The correctly simplified expression is b Plus 3r.

Answer 1

Let's simplify the expression step by step:

Given expression:
\[
(3b + 4r) + (-2b - r)
\]

1. **Distribute the addition:**
\[
3b + 4r - 2b - r
\]

2. **Combine like terms:**
- For the \(b\) terms: \(3b - 2b = 1b\) or just \(b\)
- For the \(r\) terms: \(4r - r = 3r\)

So, combining both, we have:
\[
b + 3r
\]

Therefore, Ella's result of \(b + 5r\) is incorrect because she made an error in combining the \(r\) coefficients.

The correct answer is:
**Ella incorrectly combined the r coefficients. The correctly simplified expression is \(b + 3r\).**