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After simplifying, which expressions are equivalent? Check the three that apply.(3 points) Responses −0.4b+(6b−5.9a)−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)(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−5.6b5.9a−5.6b5 point 9 A minus 5 point 6 b (2.5a+1.6b)+(3.4a+4b)(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)

1 answer

To determine which expressions are equivalent after simplification, let's simplify each expression one by one.

  1. Expression 1: −0.4b + (6b − 5.9a) \[ = -0.4b + 6b - 5.9a = (6b - 0.4b) - 5.9a = 5.6b - 5.9a \]

  2. Expression 2: (3.4a − 1.7b) + (2.5a − 3.9b) \[ = 3.4a - 1.7b + 2.5a - 3.9b = (3.4a + 2.5a) + (-1.7b - 3.9b) = 5.9a - 5.6b \]

  3. Expression 3: 5.9a − 5.6b

    • This is already simplified and is the same as the result from Expression 1 and Expression 2.

  4. Expression 4: (2.5a + 1.6b) + (3.4a + 4b) \[ = 2.5a + 1.6b + 3.4a + 4b = (2.5a + 3.4a) + (1.6b + 4b) = 5.9a + 5.6b \]

  5. Expression 5: (−3.9b + a) + (−1.7b + 4.9a) \[ = -3.9b + a - 1.7b + 4.9a = (a + 4.9a) + (-3.9b - 1.7b) = 5.9a - 5.6b \]

Now we can summarize:

  • Expression 1 simplifies to 5.6b - 5.9a
  • Expression 2 simplifies to 5.9a - 5.6b
  • Expression 3 is 5.9a - 5.6b
  • Expression 4 simplifies to 5.9a + 5.6b
  • Expression 5 simplifies to 5.9a - 5.6b

The equivalent expressions are:

  • Expression 2: 5.9a - 5.6b
  • Expression 3: 5.9a - 5.6b
  • Expression 5: 5.9a - 5.6b

So the three equivalent expressions are 2, 3, and 5.