Question

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.

Answer 1

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**.