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 7.76x

Answer 1

To simplify the expression \((7x - 2) - (0.04x - 3 + 0.2x)\), we can follow these steps:

1. Combine terms in the parentheses: \[ 0.04x - 3 + 0.2x = (0.04x + 0.2x) - 3 = 0.24x - 3 \]

2. Now substitute back into the expression: \[ (7x - 2) - (0.24x - 3) \]

3. Distribute the negative sign: \[ 7x - 2 - 0.24x + 3 \]

4. Combine like terms: \[ (7x - 0.24x) + (-2 + 3) = 6.76x + 1 \]

Thus, the simplified expression is \(6.76x + 1\).

Now we'll identify which responses match this equivalent expression:

1. \( (7x - 2) - (0.24x - 3) \): This matches the expression in a slightly rewritten form.
2. \( 7.16x - 5 \): Not equivalent.
3. \( 6.76x + 1 \): This is the same as our simplified version, thus equivalent.
4. \( 5.76x \): Not equivalent.
5. \( 7.76x \): Not equivalent.

In conclusion, the equivalent expressions are:

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

Responses:

• (7x - 2) − (0.24x - 3)
• 6.76x + 1