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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

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

(−4x−6)+(2+5x)

1 answer

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

  1. Option 1: \(-1 + (x - 4x) + 6\) \[ -1 + (x - 4x) + 6 = -1 - 3x + 6 = -3x + 5 \quad \text{(Not equivalent)} \]

  2. Option 2: \(-1 + 3x - (2x + 6)\) \[ -1 + 3x - 2x - 6 = -1 + x - 6 = x - 7 \quad \text{(Not equivalent)} \]

  3. Option 3: \((x - 7) + (2 - 4x)\) \[ (x - 7) + (2 - 4x) = x - 4x - 7 + 2 = -3x - 5 \quad \text{(Equivalent)} \]

  4. Option 4: \((-4x - 6) + (2 + 5x)\) \[ -4x - 6 + 2 + 5x = (-4x + 5x) + (-6 + 2) = x - 4 \quad \text{(Not equivalent)} \]

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