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

Question

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

−0.4b+(6b−9.5a)
negative 0 point 4 b plus open paren 6 b minus 9 point 5 A close paren

9.5a−16.4b
9 point 5 A minus 16 point 4 b

(−9.3b+a)+(−7.1b+8.5a)
open paren negative 9 point 3 b plus A close paren plus open paren negative 7 point 1 b plus 8 point 5 A close paren

(5.2a+6.1b)+(4.3a+4b)
open paren 5 point 2 A plus 6 point 1 b close paren plus open paren 4 point 3 A plus 4 b close paren

(4.3a−7.1b)+(5.2a−9.3b)

GPT-4o mini · Answer

To determine which expressions are equivalent after simplification, we can simplify each expression step-by-step:

Expression 1: \( -0.4b + (6b - 9.5a) \) \[ = -0.4b + 6b - 9.5a = (6b - 0.4b) - 9.5a = 5.6b - 9.5a \]
Expression 2: \( 9.5a - 16.4b \)
- This is already simplified.
Expression 3: \( (-9.3b + a) + (-7.1b + 8.5a) \) \[ = -9.3b + a - 7.1b + 8.5a = (-9.3b - 7.1b) + (a + 8.5a) = -16.4b + 9.5a \]
Expression 4: \( (5.2a + 6.1b) + (4.3a + 4b) \) \[ = 5.2a + 6.1b + 4.3a + 4b = (5.2a + 4.3a) + (6.1b + 4b) = 9.5a + 10.1b \]
Expression 5: \( (4.3a - 7.1b) + (5.2a - 9.3b) \) \[ = 4.3a - 7.1b + 5.2a - 9.3b = (4.3a + 5.2a) + (-7.1b - 9.3b) = 9.5a - 16.4b \]

Now let's summarize the results:

Expression 1 simplifies to \( 5.6b - 9.5a \)
Expression 2 is \( 9.5a - 16.4b \)
Expression 3 simplifies to \( 9.5a - 16.4b \)
Expression 4 simplifies to \( 9.5a + 10.1b \)
Expression 5 simplifies to \( 9.5a - 16.4b \)

From these, the equivalent expressions after simplification are:

The three expressions that are equivalent are: