Ask a New Question
Menu

After simplifying, which expressions are equivalent? Check the three that apply.



NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.

(3 points)
Responses

(4.3a−7.1b)+(5.2a−9.3b)
open paren 4 point 3 A minus 7 point 1 b close paren plus open paren 5 point 2 A minus 9 point 3 b close paren

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

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

(−9.3b+a)+(−7.1b+8.5a)

1 answer

To determine which expressions are equivalent, let's simplify each one step-by-step.

  1. Expression 1: \((4.3a - 7.1b) + (5.2a - 9.3b)\)

    Combine like terms:

    • For \(a\): \(4.3a + 5.2a = 9.5a\)
    • For \(b\): \(-7.1b - 9.3b = -16.4b\)

    Result: \(9.5a - 16.4b\)

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

    This is already simplified.

  3. Expression 3: \(-0.4b + (6b - 9.5a)\)

    Combine like terms:

    • For \(b\): \(-0.4b + 6b = 5.6b\)
    • \(a\) remains: \(-9.5a\)

    Result: \(-9.5a + 5.6b\)

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

    Combine like terms:

    • For \(a\): \(5.2a + 4.3a = 9.5a\)
    • For \(b\): \(6.1b + 4b = 10.1b\)

    Result: \(9.5a + 10.1b\)

  5. Expression 5: \((-9.3b + a) + (-7.1b + 8.5a)\)

    Combine like terms:

    • For \(a\): \(a + 8.5a = 9.5a\)
    • For \(b\): \(-9.3b - 7.1b = -16.4b\)

    Result: \(9.5a - 16.4b\)

Now we can determine equivalences:

  • Expression 1 simplifies to \(9.5a - 16.4b\).
  • Expression 2 is \(9.5a - 16.4b\) (equivalent).
  • Expression 3 simplifies to \(-9.5a + 5.6b\) (not equivalent).
  • Expression 4 simplifies to \(9.5a + 10.1b\) (not equivalent).
  • Expression 5 simplifies to \(9.5a - 16.4b\) (equivalent).

The equivalent expressions are:

  1. Expresssion 1: \(9.5a - 16.4b\)
  2. Expression 2: \(9.5a - 16.4b\)
  3. Expression 5: \(9.5a - 16.4b\)

So, the final answer would have the following three selected:

  • Expression 1
  • Expression 2
  • Expression 5