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

(3 points)
• (-3.9b + a) + (-1.7b + 4.9a)
• (2.5a + 1.6b) + (3.4a + 4b)
• -0.46 + (66 - 5.9a)
• (3.4а - 1.7b) + (2.5a - 3.9b)
• 5.9а — 5.66

1 answer

To determine which expressions are equivalent after simplification, I'll simplify each expression and compare the results.

  1. Expression 1: (-3.9b + a) + (-1.7b + 4.9a)

    • Combine like terms:
      • For \(a\): \(a + 4.9a = 5.9a\)
      • For \(b\): \(-3.9b - 1.7b = -5.6b\)
    • Result: \(5.9a - 5.6b\)

  2. Expression 2: (2.5a + 1.6b) + (3.4a + 4b)

    • Combine like terms:
      • For \(a\): \(2.5a + 3.4a = 5.9a\)
      • For \(b\): \(1.6b + 4b = 5.6b\)
    • Result: \(5.9a + 5.6b\)

  3. Expression 3: -0.46 + (66 - 5.9a)

    • Combine constants:
      • \(66 - 0.46 = 65.54\)
    • Result: \(65.54 - 5.9a\) or \(-5.9a + 65.54\)

  4. Expression 4: (3.4a - 1.7b) + (2.5a - 3.9b)

    • Combine like terms:
      • For \(a\): \(3.4a + 2.5a = 5.9a\)
      • For \(b\): \(-1.7b - 3.9b = -5.6b\)
    • Result: \(5.9a - 5.6b\)

  5. Expression 5: 5.9a - 5.66

    • This expression remains \(5.9a - 5.66\).

Now, let's compare the results:

  • Expression 1: \(5.9a - 5.6b\)
  • Expression 2: \(5.9a + 5.6b\)
  • Expression 3: \(65.54 - 5.9a\) (not equivalent)
  • Expression 4: \(5.9a - 5.6b\)
  • Expression 5: \(5.9a - 5.66\) (not equivalent)

The equivalent expressions are:

  • Expression 1: \(5.9a - 5.6b\)
  • Expression 4: \(5.9a - 5.6b\)

Therefore, the equivalent expressions are:

  1. \((-3.9b + a) + (-1.7b + 4.9a)\)
  2. \((3.4а - 1.7b) + (2.5a - 3.9b)\)

For the third equivalent expression, it does not match any of the others. Therefore, the two that are equivalent after simplifying are:

  • Expression 1 and Expression 4.

None of the other expressions match those results.