Which expression is equivalent to −3x−5

Question

?(1 point)
Responses

−1+3x−(2x+6)
negative 1 plus 3 x minus left parenthesis 2 x plus 6 right parenthesis

(x−7)+(2−4x)
left parenthesis x minus 7 right parenthesis plus left parenthesis 2 minus 4 x right parenthesis

−1+(x−4x)+6
negative 1 plus left parenthesis x minus 4 x right parenthesis plus 6

(−4x−6)+(2+5x)

Answer 1

To determine which expression is equivalent to \(-3x - 5\), we'll simplify each of the provided options.

1. Option: \(-1 + 3x - (2x + 6)\)

   Simplifying: \[ -1 + 3x - 2x - 6 = -1 + x - 6 = x - 7 \] (Not equivalent)

2. Option: \((x - 7) + (2 - 4x)\)

   Simplifying: \[ x - 7 + 2 - 4x = x - 4x - 7 + 2 = -3x - 5 \] (Equivalent)

3. Option: \(-1 + (x - 4x) + 6\)

   Simplifying: \[ -1 + x - 4x + 6 = -1 - 3x + 6 = -3x + 5 \] (Not equivalent)

4. Option: \((-4x - 6) + (2 + 5x)\)

   Simplifying: \[ -4x - 6 + 2 + 5x = -4x + 5x - 6 + 2 = x - 4 \] (Not equivalent)

The only expression that simplifies to \(-3x - 5\) is the second option:

\[ (x - 7) + (2 - 4x). \]