Question

Which expression is equivalent to -3x - 5?

-1 + (x - 4x) + 6

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

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

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

Answer 1

Let's simplify each expression to see which one is equivalent to \(-3x - 5\).

1. **Expression**: \(-1 + (x - 4x) + 6\)

Simplifying inside the parentheses:
\[
x - 4x = -3x
\]
So the expression becomes:
\[
-1 - 3x + 6
\]
Now simplify:
\[
-3x + 5
\]

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

Simplifying the expression inside the brackets:
\[
-1 + 3x - 2x - 6
\]
Combine like terms:
\[
(3x - 2x) - 1 - 6 = x - 7
\]

3. **Expression**: \((x - 7) + (2 - 4x)\)

Simplifying this expression:
\[
x - 7 + 2 - 4x
\]
Combine like terms:
\[
(x - 4x) + (-7 + 2) = -3x - 5
\]

4. **Expression**: \((-4x - 6) + (2 + 5x)\)

Simplifying this expression:
\[
-4x - 6 + 2 + 5x
\]
Combine like terms:
\[
(-4x + 5x) + (-6 + 2) = x - 4
\]

Now let's review the results:
- The first expression simplifies to \(5 - 3x\).
- The second expression simplifies to \(x - 7\).
- The third expression simplifies to \(-3x - 5\).
- The fourth expression simplifies to \(x - 4\).

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

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