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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

(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

(−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

(4.3a−7.1b)+(5.2a−9.3b)

1 answer

To determine which expressions are equivalent after simplification, let's simplify each of them step by step.

  1. Expression 1: \(-0.4b + (6b - 9.5a)\)

    Simplifying: \[ -0.4b + 6b - 9.5a = (6b - 0.4b) - 9.5a = 5.6b - 9.5a \]

  2. Expression 2: \(9.5a - 16.4b\)

    This expression is already simplified as \(9.5a - 16.4b\).

  3. Expression 3: \((5.2a + 6.1b) + (4.3a + 4b)\)

    Simplifying: \[ 5.2a + 6.1b + 4.3a + 4b = (5.2a + 4.3a) + (6.1b + 4b) = 9.5a + 10.1b \]

  4. Expression 4: \((-9.3b + a) + (-7.1b + 8.5a)\)

    Simplifying: \[ -9.3b + a - 7.1b + 8.5a = (a + 8.5a) + (-9.3b - 7.1b) = 9.5a - 16.4b \]

  5. Expression 5: \((4.3a - 7.1b) + (5.2a - 9.3b)\)

    Simplifying: \[ 4.3a - 7.1b + 5.2a - 9.3b = (4.3a + 5.2a) + (-7.1b - 9.3b) = 9.5a - 16.4b \]

Now, let's summarize the results after simplification:

  1. \(5.6b - 9.5a\)
  2. \(9.5a - 16.4b\)
  3. \(9.5a + 10.1b\)
  4. \(9.5a - 16.4b\)
  5. \(9.5a - 16.4b\)

The equivalent expressions are:

  • Expression 2: \(9.5a - 16.4b\)
  • Expression 4: \(9.5a - 16.4b\)
  • Expression 5: \(9.5a - 16.4b\)

Thus, the correct responses to select are:

  • \(9.5a - 16.4b\)
  • \((-9.3b + a) + (-7.1b + 8.5a)\)
  • \((4.3a - 7.1b) + (5.2a - 9.3b)\)