Question

10. A student solves the following equation:

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.