10. A student solves the following equation:

Question

Problem: 2(x−3)+3x=19

Step 1: 2x−6+3x=19

Step 2: (2x+3x)−6=19

Step 3: 5x−6=19

Step 4: 5x−6+6=19+6

Step 5: 5x=25

Step 6: x=5

Answer 1

The student has correctly solved the equation step-by-step. Here's a breakdown of each step:

1. Start with the original equation:
   \[ 2(x - 3) + 3x = 19 \]

2. Distribute the 2:
   \[ 2x - 6 + 3x = 19 \]
   (Step 1 is correct)

3. Combine like terms:
   \[ (2x + 3x) - 6 = 19 \]
   \[ 5x - 6 = 19 \]
   (Step 2 and Step 3 are correct)

4. Add 6 to both sides:
   \[ 5x - 6 + 6 = 19 + 6 \]
   \[ 5x = 25 \]
   (Step 4 and Step 5 are correct)

5. Divide by 5:
   \[ x = \frac{25}{5} \]
   \[ x = 5 \]
   (Step 6 is correct)

The final solution is \( x = 5 \). The student followed the correct steps to arrive at the solution.