\( 3(x+2)=3 x+6 \) \( 3 x+2 x=x^{2}(3+2) \) \( 3 x+2=3(x+2) \) \( -3(2+x)=-6 x-3 \) Which pair shows equivalent expressions? 3

Let's analyze each of the given equations to determine which pair consists of equivalent expressions: 1. **\( 3(x + 2) = 3x + 6 \)** - **Left Side (LS):** \( 3(x + 2) \) - **Right Side (RS):** \( 3x + 6 \) - **Verification:** Distributing the 3 on the left side: \[ 3(x + 2) = 3x + 6 \] This shows that both sides are indeed equivalent. 2. **\( 3x + 2x = x^{2}(3 + 2) \)** - **Left Side (LS):** \( 3x + 2x = 5x \) - **Right Side (RS):** \( x^{2}(3 + 2) = 5x^2 \) - **Verification:** The left side simplifies to \( 5x \) and the right side to \( 5x^2 \). These are **not** equivalent unless \( x = 0 \) or \( x = 1 \). 3. **\( 3x + 2 = 3(x + 2) \)** - **Left Side (LS):** \( 3x + 2 \) - **Right Side (RS):** \( 3x + 6 \) - **Verification:** Subtracting \( 3x \) from both sides: \[ 2 = 6 \] This is a false statement, so the expressions are **not** equivalent. 4. **\( -3(2 + x) = -6x - 3 \)** - **Left Side (LS):** \( -3(2 + x) = -6 - 3x \) - **Right Side (RS):** \( -6x - 3 \) - **Verification:** Comparing both sides: \[ -6 - 3x \quad \text{vs.} \quad -6x - 3 \] These are **not** equivalent. **Conclusion:** Only the **first pair** \( 3(x + 2) = 3x + 6 \) consists of equivalent expressions.