Solve the following equation. \[ -\frac{x}{5}-3=1+\frac{x}{5} \]

To solve the equation: \[ -\frac{x}{5} - 3 = 1 + \frac{x}{5} \] **Step 1: Eliminate the Fractions** Multiply every term by 5 to eliminate the denominators: \[ 5 \left( -\frac{x}{5} \right) - 5 \times 3 = 5 \times 1 + 5 \left( \frac{x}{5} \right) \] Simplifying each term: \[ - x - 15 = 5 + x \] **Step 2: Get All \( x \)-Terms on One Side** Add \( x \) to both sides to move all \( x \)-terms to the right: \[ -15 = 5 + x + x \] \[ -15 = 5 + 2x \] **Step 3: Isolate \( x \)** Subtract 5 from both sides: \[ -15 - 5 = 2x \] \[ -20 = 2x \] Divide both sides by 2: \[ x = \frac{-20}{2} \] \[ x = -10 \] **Solution:** \[ x = -10 \]