Question

After simplifying, which expressions are equivalent? Check the three that apply.
A. -0.4b+(6b-5.9a)
B. (3.4a - 1.7b) + (2.5a - 3.9b)
C. (2.5a + 1.6b) + (3.4a+4b)
D. 5.9a - 5.6b
E. (-3.9b+a) + (-1.7b + 4.9a)

Answer 1

To determine which expressions are equivalent after simplification, we'll simplify each expression step by step.

### Expression A:
\[
-0.4b + (6b - 5.9a)
\]
Distributing and combining like terms:
\[
6b - 0.4b - 5.9a = 5.6b - 5.9a
\]

### Expression B:
\[
(3.4a - 1.7b) + (2.5a - 3.9b)
\]
Combining like terms:
\[
3.4a + 2.5a - 1.7b - 3.9b = (3.4 + 2.5)a + (-1.7 - 3.9)b = 5.9a - 5.6b
\]

### Expression C:
\[
(2.5a + 1.6b) + (3.4a + 4b)
\]
Combining like terms:
\[
2.5a + 3.4a + 1.6b + 4b = (2.5 + 3.4)a + (1.6 + 4)b = 5.9a + 5.6b
\]

### Expression D:
\[
5.9a - 5.6b
\]
This is already in its simplest form.

### Expression E:
\[
(-3.9b + a) + (-1.7b + 4.9a)
\]
Combining like terms:
\[
(-3.9b - 1.7b) + (a + 4.9a) = (-3.9 - 1.7)b + (1 + 4.9)a = -5.6b + 5.9a
\]

### Summary of Results:
- A simplifies to \(5.6b - 5.9a\)
- B simplifies to \(5.9a - 5.6b\)
- C simplifies to \(5.9a + 5.6b\)
- D is \(5.9a - 5.6b\)
- E simplifies to \(5.9a - 5.6b\)

The equivalent expressions are:
- **B**: \(5.9a - 5.6b\)
- **D**: \(5.9a - 5.6b\)
- **E**: \(5.9a - 5.6b\)

So the three expressions you should check as equivalent are **B**, **D**, and **E**.