Question

Select ALL equivalent expressions to: (7𝑥 ― 2) ― (0.04𝑥 ― 3 + 0.2𝑥) (2 points) Responses (7x − 2) − (0.24x − 3) (7x negative 2) negative (0.24x negative 3) 7.16x − 5 7.16x negative5 6.76x + 1 6.76x plus 1 5.76x 5.76x 7.76x

Answer 1

Let's simplify the expression step by step.

The original expression is:

\[
(7x - 2) - (0.04x - 3 + 0.2x)
\]

First, simplify the expression inside the parentheses:

\[
0.04x - 3 + 0.2x = (0.04x + 0.2x) - 3 = 0.24x - 3
\]

Now substitute this back into the expression:

\[
(7x - 2) - (0.24x - 3)
\]

Distributing the negative sign:

\[
(7x - 2) - 0.24x + 3
\]

Combine like terms:

\[
7x - 0.24x - 2 + 3 = (7x - 0.24x) + (3 - 2)
\]

This simplifies to:

\[
(7 - 0.24)x + 1 = 6.76x + 1
\]

Now let's look at the options provided:

1. \( (7x - 2) - (0.24x - 3) \) – This matches the step we took, as we simplified.
2. \( 7.16x - 5 \) – Incorrect.
3. \( 6.76x + 1 \) – This is correct.
4. \( 5.76x \) – Incorrect.
5. \( 7.76x \) – Incorrect.

Therefore, the equivalent expressions are:

- \( (7x - 2) - (0.24x - 3) \)
- \( 6.76x + 1 \)

So the responses are:

- \( (7x - 2) - (0.24x - 3) \)
- \( 6.76x + 1 \)