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

Answer 1

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

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

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

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

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

Now, let's summarize the results:
- Option 1 simplifies to \(-3x - 5\) (this is equivalent).
- Option 2 simplifies to \(x - 4\) (not equivalent).
- Option 3 simplifies to \(x - 7\) (not equivalent).
- Option 4 simplifies to \(-3x + 5\) (not equivalent).

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