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Determine which expressions are equivalent to 0.87 – 4.5 – [5.8 + (-7.8)]. (Choose 2.)Responses 0.87 – 4.5 + (-5.8) + 7.8 0.87 – 4.5 + (-5.8) + 7.8 - this question requires at least 2 answersB0.87 + 4.5 – 5.8 + 7.80.87 + 4.5 – 5.8 + 7.8 - this question requires at least 2 answers.87 – 4.5 – 5.8 + 7.80.87 – 4.5 – 5.8 + 7.8 - this question requires at least 2 answersD0.87 + 4.5 + 5.8 – 7.80.87 + 4.5 + 5.8 – 7.8 - this question requires at least 2 answersE0.87 – 4.5 + 5.8 - 7.80.87 – 4.5 + 5.8 - 7.8 - this question requires at least 2 answersThis question requires at least 2 answers.

1 answer

To determine which expressions are equivalent to \(0.87 - 4.5 - [5.8 + (-7.8)]\), we first simplify the original expression.

  1. Start with the expression inside the brackets: \[ 5.8 + (-7.8) = 5.8 - 7.8 = -2.0 \]

  2. Substitute back into the original expression: \[ 0.87 - 4.5 - (-2.0) = 0.87 - 4.5 + 2.0 \]

  3. Now simplify \(0.87 - 4.5 + 2.0\): \[ 0.87 - 4.5 = -3.63 \] \[ -3.63 + 2.0 = -1.63 \]

Now that we have simplified the original expression to \(-1.63\), we will examine the provided options to find two expressions that also evaluate to \(-1.63\).

Let's evaluate each option:

A) \(0.87 - 4.5 + (-5.8) + 7.8\)

  • Simplifying: \[ 0.87 - 4.5 - 5.8 + 7.8 \]
  • This simplifies to: \[ 0.87 - 4.5 + 7.8 - 5.8 = 0.87 - 4.5 + 2.0 = -1.63 \quad \text{(equivalent)} \]

B) \(0.87 + 4.5 - 5.8 + 7.8\)

  • Simplifying: \[ 0.87 + 4.5 - 5.8 + 7.8 \]
  • This simplifies to: \[ 0.87 + 4.5 + 7.8 - 5.8 = 0.87 + 6.5 = 7.37 \quad \text{(not equivalent)} \]

C) \(0.87 - 4.5 - 5.8 + 7.8\)

  • Simplifying: \[ 0.87 - 4.5 - 5.8 + 7.8 \]
  • This simplifies to: \[ 0.87 - 10.3 + 7.8 = 0.87 - 2.5 = -1.63 \quad \text{(equivalent)} \]

D) \(0.87 + 4.5 + 5.8 - 7.8\)

  • Simplifying: \[ 0.87 + 4.5 + 5.8 - 7.8 \]
  • This simplifies to: \[ 0.87 + 4.5 + 5.8 - 7.8 = 0.87 + 2.0 = 2.87 \quad \text{(not equivalent)} \]

E) \(0.87 - 4.5 + 5.8 - 7.8\)

  • Simplifying: \[ 0.87 - 4.5 + 5.8 - 7.8 \]
  • This simplifies to: \[ 0.87 - 4.5 - 2.0 = 0.87 - 6.5 = -5.63 \quad \text{(not equivalent)} \]

The two equivalent expressions are:

  1. \(0.87 - 4.5 + (-5.8) + 7.8\) (Option A)
  2. \(0.87 - 4.5 - 5.8 + 7.8\) (Option C)

Thus, the final answers are A and C.