Which expression is equivalent to -3x - 5?

Question

-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:

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