Question

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

Answer 1

To determine which expression is equivalent to \(-3x - 5\), let's simplify each of the given options:

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

   Simplifying: \[ -4x - 6 + 2 + 5x = (-4x + 5x) + (-6 + 2) = 1x - 4 = x - 4 \] This is not equivalent.

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

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

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

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

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

   Simplifying: \[ (x - 7) + (2 - 4x) = x - 7 + 2 - 4x = (x - 4x) + (-7 + 2) = -3x - 5 \] This is equivalent to \(-3x - 5\).

Thus, the expression that is equivalent to \(-3x - 5\) is:

\[ \boxed{(x - 7) + (2 - 4x)} \]