Question

After simplifying, which expressions are equivalent? Check the three that apply.(3 points)
Responses

(−3.9b+a)+(−1.7b+4.9a)
open paren negative 3 point 9 b plus A close paren plus open paren negative 1 point 7 b plus 4 point 9 A close paren

(2.5a+1.6b)+(3.4a+4b)
open paren 2 point 5 A plus 1 point 6 b close paren plus open paren 3 point 4 A plus 4 b close paren

5.9a−5.6b
5 point 9 A minus 5 point 6 b

−0.4b+(6b−5.9a)
negative 0 point 4 b plus open paren 6 b minus 5 point 9 A close paren

(3.4a−1.7b)+(2.5a−3.9b)

Answer 1

To determine which expressions are equivalent, let’s simplify each expression step by step.

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

2. **Second Expression:**
\[
(2.5a + 1.6b) + (3.4a + 4b)
\]
Combining like terms:
\[
= 2.5a + 3.4a + 1.6b + 4b
= 5.9a + 5.6b
\]

3. **Third Expression:**
\[
5.9a - 5.6b
\]
This is simplified as it stands.

4. **Fourth Expression:**
\[
-0.4b + (6b - 5.9a)
\]
Combining like terms:
\[
= -0.4b + 6b - 5.9a
= 5.6b - 5.9a
\]
Note that this can be rearranged to:
\[
= -5.9a + 5.6b
\]

5. **Fifth Expression:**
\[
(3.4a - 1.7b) + (2.5a - 3.9b)
\]
Combining like terms:
\[
= 3.4a + 2.5a - 1.7b - 3.9b
= 5.9a - 5.6b
\]

Now let’s summarize the results:
- First Expression simplifies to \( 5.9a - 5.6b \)
- Second Expression simplifies to \( 5.9a + 5.6b \)
- Third Expression is \( 5.9a - 5.6b \)
- Fourth Expression simplifies to \( -5.9a + 5.6b \)
- Fifth Expression simplifies to \( 5.9a - 5.6b \)

From the above, the equivalent expressions are:
- **First Expression:** \( 5.9a - 5.6b \)
- **Third Expression:** \( 5.9a - 5.6b \)
- **Fifth Expression:** \( 5.9a - 5.6b \)

Therefore, the three expressions that are equivalent are:
1. \( (-3.9b + a) + (-1.7b + 4.9a) \)
2. \( 5.9a - 5.6b \)
3. \( (3.4a - 1.7b) + (2.5a - 3.9b) \)

Please note that the second expression \( 5.9a + 5.6b \) and the fourth expression \( -5.9a + 5.6b \) are not equivalent to the others.