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−5.9a)
negative 0 point 4 b plus open paren 6 b minus 5 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

(−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

(3.4a−1.7b)+(2.5a−3.9b)
open paren 3 point 4 A minus 1 point 7 b close paren plus open paren 2 point 5 A minus 3 point 9 b close paren

5.9a−5.6b

GPT-4o mini · Answer

Let's simplify each expression to determine which are equivalent.

Expression 1: \(-0.4b + (6b - 5.9a)\) Simplifying this gives: \[ -0.4b + 6b - 5.9a = (6b - 0.4b) - 5.9a = 5.6b - 5.9a \]
Expression 2: \((2.5a + 1.6b) + (3.4a + 4b)\) Simplifying this gives: \[ 2.5a + 1.6b + 3.4a + 4b = (2.5a + 3.4a) + (1.6b + 4b) = 5.9a + 5.6b \]
Expression 3: \((-3.9b + a) + (-1.7b + 4.9a)\) Simplifying this gives: \[ -3.9b + a - 1.7b + 4.9a = (-3.9b - 1.7b) + (a + 4.9a) = -5.6b + 5.9a \]
Expression 4: \((3.4a - 1.7b) + (2.5a - 3.9b)\) Simplifying this gives: \[ 3.4a - 1.7b + 2.5a - 3.9b = (3.4a + 2.5a) + (-1.7b - 3.9b) = 5.9a - 5.6b \]
Expression 5: \(5.9a - 5.6b\) This expression is already simplified.

Now let's summarize the simplified forms:

Expression 1 simplifies to \(5.6b - 5.9a\)
Expression 2 simplifies to \(5.9a + 5.6b\)
Expression 3 simplifies to \(-5.6b + 5.9a\)
Expression 4 simplifies to \(5.9a - 5.6b\)
Expression 5 is \(5.9a - 5.6b\)

We can see that:

Expression 4 and Expression 5 are equivalent (both simplify to \(5.9a - 5.6b\)).
Expression 3 simplifies to \(-5.6b + 5.9a\), which is equivalent to Expression 4 (since they are rearrangements).

Therefore, the equivalent expressions are:

Final equivalent expressions are:

So the answer is: Expressions 3, 4, and 5.