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:
- \( (7x - 2) - (0.24x - 3) \) – This matches the step we took, as we simplified.
- \( 7.16x - 5 \) – Incorrect.
- \( 6.76x + 1 \) – This is correct.
- \( 5.76x \) – Incorrect.
- \( 7.76x \) – Incorrect.
Therefore, the equivalent expressions are:
- \( (7x - 2) - (0.24x - 3) \)
- \( 6.76x + 1 \)
So the responses are:
- \( (7x - 2) - (0.24x - 3) \)
- \( 6.76x + 1 \)