Solve the equations by trial-and-error method.
`3x+8=44`

Answer

To solve the equation \(3x + 8 = 44\) using the trial-and-error method, we will substitute different values for \(x\) until we find the one that makes the left-hand side (LHS) equal to the right-hand side (RHS).

### Step-by-Step Solution:

1. **Start with the equation**:
\[ 3x + 8 = 44 \]

2. **Substitute \(x = 1\)**:
\[ LHS = 3(1) + 8 = 3 + 8 = 11 \]
This is not equal to 44.

3. **Substitute \(x = 2\)**:
\[ LHS = 3(2) + 8 = 6 + 8 = 14 \]
This is not equal to 44.

4. **Substitute \(x = 3\)**:
\[ LHS = 3(3) + 8 = 9 + 8 = 17 \]
This is not equal to 44.

5. **Substitute \(x = 4\)**:
\[ LHS = 3(4) + 8 = 12 + 8 = 20 \]
This is not equal to 44.

6. **Substitute \(x = 5\)**:
\[ LHS = 3(5) + 8 = 15 + 8 = 23 \]
This is not equal to 44.

7. **Substitute \(x = 6\)**:
\[ LHS = 3(6) + 8 = 18 + 8 = 26 \]
This is not equal to 44.

8. **Substitute \(x = 7\)**:
\[ LHS = 3(7) + 8 = 21 + 8 = 29 \]
This is not equal to 44.

9. **Substitute \(x = 8\)**:
\[ LHS = 3(8) + 8 = 24 + 8 = 32 \]
This is not equal to 44.

10. **Substitute \(x = 9\)**:
\[ LHS = 3(9) + 8 = 27 + 8 = 35 \]
This is not equal to 44.

11. **Substitute \(x = 10\)**:
\[ LHS = 3(10) + 8 = 30 + 8 = 38 \]
This is not equal to 44.

12. **Substitute \(x = 11\)**:
\[ LHS = 3(11) + 8 = 33 + 8 = 41 \]
This is not equal to 44.

13. **Substitute \(x = 12\)**:
\[ LHS = 3(12) + 8 = 36 + 8 = 44 \]
This is equal to 44.

### Conclusion:
The value of \(x\) that satisfies the equation \(3x + 8 = 44\) is:
\[ \boxed{12} \]