To determine if \( 2a + b \equiv 0 \pmod{3} \), let's analyze the expression. 

### What it means:
The congruence \( 2a + b \equiv 0 \pmod{3} \) implies that the remainder when \( 2a + b \) is divided by 3 is zero. In other words, \( 2a + b \) must be divisible by 3.

### Steps to check:
1. Simplify \( 2a + b \mod 3 \):
   - \( 2a + b \mod 3 \) means the sum \( 2a + b \) is reduced modulo 3.
   - If \( 2a \mod 3 \) and \( b \mod 3 \) are known, you can add the results and reduce modulo 3 to check if the sum equals 0.

2. Verify divisibility:
   - If \( a \) and \( b \) are integers, evaluate \( 2a \mod 3 \) and \( b \mod 3 \) individually. Substitute into the equation to confirm the congruence.

### Example:
- If \( a = 1 \) and \( b = 1 \), calculate:
  \[
  2a + b = 2(1) + 1 = 3 \equiv 0 \pmod{3}.
  \]
  So the congruence holds for this example.

For a generalized answer:
- The congruence \( 2a + b \equiv 0 \pmod{3} \) holds true only if \( 2a + b \) is divisible by 3.

Let me know if you’d like me to evaluate this further or provide specific examples!

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### 5 Questions to Expand Understanding:
1. What values of \( a \) and \( b \) satisfy \( 2a + b \equiv 0 \pmod{3} \)?
2. How does modular arithmetic affect solving linear equations?
3. Can we generalize this solution for other moduli (e.g., mod 4 or mod 5)?
4. What are some applications of modular arithmetic in real-world problems?
5. How can systems of congruences (e.g., simultaneous modular equations) be solved?

### Tip:
Always simplify individual terms modulo \( n \) before combining them in modular arithmetic—it makes calculations faster and reduces errors.

Explore the solution to the modular arithmetic problem 2a + b ≡ 0 mod 3. Learn key concepts, including linear congruences and properties of modular arithmetic, with step-by-step explanations. Suitable for Grades 9-12.

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