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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

1 answer

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:

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