Question

Question

Which expression is equivalent to −3x−5
?(1 point)
Responses

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

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

(−4x−6)+(2+5x)
left parenthesis negative 4 x minus 6 right parenthesis plus left parenthesis 2 plus 5 x right parenthesis

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

Answer 1

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

1. Option 1: \[ -1 + (x - 4x) + 6 \] Simplifying this: \[ -1 + (x - 4x) + 6 = -1 - 3x + 6 = -3x + 5 \] This is not equivalent to \(-3x - 5\).

2. Option 2: \[ -1 + 3x - (2x + 6) \] Simplifying this: \[ -1 + 3x - 2x - 6 = -1 + x - 6 = x - 7 \] This is not equivalent to \(-3x - 5\).

3. Option 3: \[ (-4x - 6) + (2 + 5x) \] Simplifying this: \[ -4x - 6 + 2 + 5x = (-4x + 5x) + (-6 + 2) = x - 4 \] This is not equivalent to \(-3x - 5\).

4. Option 4: \[ (x - 7) + (2 - 4x) \] Simplifying this: \[ x - 7 + 2 - 4x = (x - 4x) + (-7 + 2) = -3x - 5 \] This expression simplifies to \(-3x - 5\).

Thus, the expression that is equivalent to \(-3x - 5\) is Option 4: \((x - 7) + (2 - 4x)\).