If 2a + 4 = 8, then find the value of 3a + 6.

Concept: To evaluate an algebraic expression when a linear equation is given in the same variable, first solve the equation to isolate the variable, then substitute that value into the target expression. When the target expression is a constant multiple of the given equation, it can also be evaluated directly by scaling, without solving for the variable at all.

Application:

1. Start with the given equation: 2a + 4 = 8.

2. Subtract 4 from both sides: 2a = 8 − 4 = 4.

3. Divide both sides by 2: a = 4 ÷ 2 = 2.

4. Substitute a = 2 into the target expression 3a + 6: 3(2) + 6.

5. Simplify: 6 + 6 = 12.

Cross-check: Since 3a + 6 = 1.5 × (2a + 4), and 2a + 4 = 8, the expression equals 1.5 × 8 = 12 directly — this matches the substitution result and confirms it independently.

Result: The value of 3a + 6 is 12.