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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

(−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

(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

5.9a−5.6b

1 answer

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

  1. Expression 1: \(-0.4b + (6b - 5.9a)\)

    • Distributing the parentheses: \[ -0.4b + 6b - 5.9a = (6b - 0.4b) - 5.9a = 5.6b - 5.9a \]

  2. Expression 2: \((-3.9b + a) + (-1.7b + 4.9a)\)

    • Grouping like terms: \[ (-3.9b - 1.7b) + (a + 4.9a) = -5.6b + 5.9a \]

  3. Expression 3: \((3.4a - 1.7b) + (2.5a - 3.9b)\)

    • Grouping like terms: \[ (3.4a + 2.5a) + (-1.7b - 3.9b) = 5.9a - 5.6b \]

  4. Expression 4: \((2.5a + 1.6b) + (3.4a + 4b)\)

    • Grouping like terms: \[ (2.5a + 3.4a) + (1.6b + 4b) = 5.9a + 5.6b \]

  5. Expression 5: \(5.9a - 5.6b\)

Summary of Results:

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

Now to find equivalent expressions:

  • Expressions 2 and 3 are equivalent, as both simplify to \(5.9a - 5.6b\), where Expression 2 is just the negative of the b-term.

Therefore, the expressions that are equivalent are:

  1. Expression 3: \((3.4a - 1.7b) + (2.5a - 3.9b)\)
  2. Expression 2: \((-3.9b + a) + (-1.7b + 4.9a)\)
  3. Expression 5: \(5.9a - 5.6b\)

The three that apply are:

  • Expression 2
  • Expression 3
  • Expression 5