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
negative 1 plus left parenthesis x minus 4 x right parenthesis plus 6

Answer 1

To find which expression is equivalent to \(-3x - 5\), we will simplify each option.

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

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

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

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

Now we summarize the results:
- Option 1 simplifies to \(-3x - 5\).
- Option 2 simplifies to \(x - 4\).
- Option 3 simplifies to \(x - 7\).
- Option 4 simplifies to \(-3x + 5\).

The only option that simplifies to \(-3x - 5\) is **Option 1: \((x - 7) + (2 - 4x)\)**.