Question

Which expression is equivalent to −3x−5 ?

A, -1+(x-4x)+6

B, (x-7)+(2-4x)

C, (-4x-6)+(2+5x)

D, -1+3x-(2x+6)

Answer 1

To determine which expression is equivalent to \(-3x - 5\), we need to simplify each option and compare it to \(-3x - 5\).

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

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

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

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

Now comparing the simplified expressions:

- A simplifies to \(-3x + 5\)
- B simplifies to \(-3x - 5\) (this is equivalent to our original expression)
- C simplifies to \(x - 4\)
- D simplifies to \(x - 7\)

The expression which is equivalent to \(-3x - 5\) is **Option B**.