Which is an algebraic equation?

An algebraic equation is a mathematical statement that asserts the equality of two expressions and contains at least one variable. In this case, the option that represents an algebraic equation is the one that includes an equal sign and can be evaluated as true or false.

The first choice, which states 3(9−4) = 5(4−1), illustrates this definition clearly as it shows two expressions on either side of an equals sign. After evaluating, both sides simplify to the same numerical value, demonstrating that this is indeed a valid algebraic equation.

The remaining options do not qualify as algebraic equations. The second choice, 4x−2y+8, is an algebraic expression but lacks an equals sign, which means it does not assert a relationship between two terms. The third choice, 7+5−(12/3), simplifies to a number but, again, does not represent an equation since it does not include an equals sign. Lastly, the fourth choice, 6n+2, is also an expression, as it does not contain an equality statement.

Therefore, the correct answer, establishing an equality between two expressions, is the first option.