Question

Which expression is equivalent to −3x−5 ?(1 point) Responses (x−7)+(2−4x) left parenthesis x minus 7 right parenthesis plus left parenthesis 2 minus 4 x right parenthesis (−4x−6)+(2+5x) left parenthesis negative 4 x minus 6 right parenthesis plus left parenthesis 2 plus 5 x right parenthesis −1+3x−(2x+6) negative 1 plus 3 x minus left parenthesis 2 x plus 6 right parenthesis −1+(x−4x)+6

Answer 1

To determine which expression is equivalent to \(-3x - 5\), let's simplify each of the provided options one by one.

1. Option 1: \((x - 7) + (2 - 4x)\) \[ = x - 7 + 2 - 4x \ = x - 4x - 7 + 2 \ = -3x - 5 \]

2. Option 2: \((-4x - 6) + (2 + 5x)\) \[ = -4x - 6 + 2 + 5x \ = -4x + 5x - 6 + 2 \ = 1x - 4 \ = x - 4 \]

3. Option 3: \(-1 + 3x - (2x + 6)\) \[ = -1 + 3x - 2x - 6 \ = 3x - 2x - 1 - 6 \ = 1x - 7 \ = x - 7 \]

4. Option 4: \(-1 + (x - 4x) + 6\) \[ = -1 + x - 4x + 6 \ = -1 + (1x - 4x) + 6 \ = -1 - 3x + 6 \ = -3x + 5 \]

Now, let's summarize the results:

• Option 1 simplifies to \(-3x - 5\) (this is equivalent).
• Option 2 simplifies to \(x - 4\) (not equivalent).
• Option 3 simplifies to \(x - 7\) (not equivalent).
• Option 4 simplifies to \(-3x + 5\) (not equivalent).

The expression that is equivalent to \(-3x - 5\) is Option 1: \((x - 7) + (2 - 4x)\).