3. Removing the grouping symbols, in other words, using the distributive property to eliminate the parentheses, can be challenging. List whether or not the distribution is correct. If not correct, state why it is not correct for the following equation with parentheses: \( -5(x+4)+2-(5 x-8)=-24 \) List if Correct, if not correct then state why incorrect. 3A: \( \quad-5 x+20+2-5 x \) +8 \( =-24 \) 3B: \( \quad-5 x-20-2-5 x+ \) 8 \( =-24 \) 3C: \( \quad-5 x-20-10-5 x \) \( +8=-24 \) 3D: \( \quad-5 x-20+2-5 x- \) \( 8=-24 \) 3E: \( \quad-5 x-20+2-5 x+ \) \( 8=-24 \)

Let's evaluate each distribution (3A to 3E) for the equation: \[ -5(x + 4) + 2 - (5x - 8) = -24 \] **Correct Distribution Process:** 1. **Distribute \(-5\) to \((x + 4)\):** \[ -5 \cdot x = -5x \] \[ -5 \cdot 4 = -20 \] So, \(-5(x + 4) = -5x - 20\). 2. **Distribute \(-1\) to \((5x - 8)\):** \[ -1 \cdot 5x = -5x \] \[ -1 \cdot (-8) = +8 \] So, \(- (5x - 8) = -5x + 8\). 3. **Combine all terms:** \[ -5x - 20 + 2 - 5x + 8 = -24 \] Simplify: \[ -10x - 10 = -24 \] --- ### Evaluation of Each Option: **3A:** \[ -5x + 20 + 2 - 5x + 8 = -24 \] - **Status:** ❌ **Incorrect** - **Reason:** - The distribution of \(-5(x + 4)\) is incorrectly performed. It should be \(-5x - 20\), not \(-5x + 20\). --- **3B:** \[ -5x - 20 - 2 - 5x + 8 = -24 \] - **Status:** ❌ **Incorrect** - **Reason:** - The constant \(+2\) is incorrectly distributed as \(-2\). --- **3C:** \[ -5x - 20 - 10 - 5x + 8 = -24 \] - **Status:** ❌ **Incorrect** - **Reason:** - The constants are miscalculated. The \(+2\) and \(+8\) should combine to \(+10\), not \(-10\). --- **3D:** \[ -5x - 20 + 2 - 5x - 8 = -24 \] - **Status:** ❌ **Incorrect** - **Reason:** - The distribution of \(-(5x - 8)\) is incorrect. It should be \(-5x + 8\), not \(-5x - 8\). --- **3E:** \[ -5x - 20 + 2 - 5x + 8 = -24 \] - **Status:** ✔️ **Correct** --- ### Summary: - **Correct Distribution:** **3E** - **Incorrect Distributions:** **3A, 3B, 3C, 3D** Each incorrect option fails due to improper application of the distributive property, either by incorrectly handling the signs or miscalculating the constants.