Question

Accoring to the Associative Property, which expression is equivalent to −5x−12
?(1 point)
Responses

−6+4x−(3x+18)
negative 6 plus 4 x minus open paren 3 x plus 18 close paren

−4+(2x−3x)−7
negative 4 plus open paren 2 x minus 3 x close paren minus 7

(−3x−16)+(4−2x)
open paren negative 3 x minus 16 close paren plus open paren 4 minus 2 x close paren

(9−2x)+(3−3x)

Answer 1

To identify which expression is equivalent to \(-5x - 12\) using the Associative Property, let's simplify each option step by step.

1. **Option**: \(-6 + 4x - (3x + 18)\)
- Simplify the expression:
\[
-6 + 4x - 3x - 18 = -6 + 4x - 3x - 18 = -6 - 18 + (4x - 3x) = -24 + x
\]
- This equals \(-24 + x\), which is not equivalent to \(-5x - 12\).

2. **Option**: \(-4 + (2x - 3x) - 7\)
- Simplify the expression:
\[
-4 + (2x - 3x) - 7 = -4 - x - 7 = -11 - x
\]
- This equals \(-11 - x\), which is not equivalent to \(-5x - 12\).

3. **Option**: \((-3x - 16) + (4 - 2x)\)
- Simplify the expression:
\[
-3x - 16 + 4 - 2x = -3x - 2x - 16 + 4 = -5x - 12
\]
- This equals \(-5x - 12\), which is equivalent to our original expression.

4. **Option**: \((9 - 2x) + (3 - 3x)\)
- Simplify the expression:
\[
9 - 2x + 3 - 3x = (9 + 3) + (-2x - 3x) = 12 - 5x
\]
- This equals \(12 - 5x\), which is not equivalent to \(-5x - 12\).

Based on the simplifications, the only expression that is equivalent to \(-5x - 12\) is:

**Option 3**: \((-3x - 16) + (4 - 2x)\).