Question

After simplifying, which expressions are equivalent? Check the three that apply.
(3 points)
• (-3.9b + a) + (-1.7b + 4.9a)
• (2.5a + 1.6b) + (3.4a + 4b)
• -0.46 + (66 - 5.9a)
• (3.4а - 1.7b) + (2.5a - 3.9b)
• 5.9а — 5.66

Answer 1

To determine which expressions are equivalent after simplification, I'll simplify each expression and compare the results.

1. **Expression 1: (-3.9b + a) + (-1.7b + 4.9a)**
- Combine like terms:
- For \(a\): \(a + 4.9a = 5.9a\)
- For \(b\): \(-3.9b - 1.7b = -5.6b\)
- Result: \(5.9a - 5.6b\)

2. **Expression 2: (2.5a + 1.6b) + (3.4a + 4b)**
- Combine like terms:
- For \(a\): \(2.5a + 3.4a = 5.9a\)
- For \(b\): \(1.6b + 4b = 5.6b\)
- Result: \(5.9a + 5.6b\)

3. **Expression 3: -0.46 + (66 - 5.9a)**
- Combine constants:
- \(66 - 0.46 = 65.54\)
- Result: \(65.54 - 5.9a\) or \(-5.9a + 65.54\)

4. **Expression 4: (3.4a - 1.7b) + (2.5a - 3.9b)**
- Combine like terms:
- For \(a\): \(3.4a + 2.5a = 5.9a\)
- For \(b\): \(-1.7b - 3.9b = -5.6b\)
- Result: \(5.9a - 5.6b\)

5. **Expression 5: 5.9a - 5.66**
- This expression remains \(5.9a - 5.66\).

Now, let's compare the results:

- **Expression 1**: \(5.9a - 5.6b\)
- **Expression 2**: \(5.9a + 5.6b\)
- **Expression 3**: \(65.54 - 5.9a\) (not equivalent)
- **Expression 4**: \(5.9a - 5.6b\)
- **Expression 5**: \(5.9a - 5.66\) (not equivalent)

The equivalent expressions are:

- Expression 1: \(5.9a - 5.6b\)
- Expression 4: \(5.9a - 5.6b\)

Therefore, the equivalent expressions are:
1. \((-3.9b + a) + (-1.7b + 4.9a)\)
4. \((3.4а - 1.7b) + (2.5a - 3.9b)\)

For the third equivalent expression, it does not match any of the others. Therefore, the two that are equivalent after simplifying are:

- **Expression 1** and **Expression 4**.

None of the other expressions match those results.