The Correct Answer and Explanation is:
The correct answer is 12.
To understand why 12 is the constant, we must first break down the given algebraic expression, which is 4x + y + 6z + 12. An algebraic expression is a mathematical phrase composed of numbers, variables, and operational symbols like addition or subtraction. The parts of the expression that are separated by these operational signs are called terms. In this specific expression, we can identify four distinct terms: the first is 4x, the second is y, the third is 6z, and the fourth is 12.
A constant is a specific type of term within an expression. Its defining characteristic is that it has a fixed value which does not change. A key way to identify a constant is to look for a term that does not contain any variables, such as x, y, or z. The value of a constant remains the same regardless of the values that might be assigned to the variables elsewhere in the expression. Let’s examine each term individually to pinpoint the constant.
The first term is 4x. This term consists of a number, 4, multiplied by a variable, x. The number 4 is called the coefficient, and x is the variable. Because the overall value of this term depends directly on the value of x, it is not a constant. For instance, if x were 2, the term’s value would be 8, but if x were 3, the term’s value would become 12. Since its value can vary, it is a variable term.
The second term is y. This is a variable standing alone. Its value can change, so it is not a constant. Likewise, the third term, 6z, contains the variable z. Its value is entirely dependent on whatever numerical value z represents, so it is also classified as a variable term.
Finally, we consider the last term, 12. This term is a number that stands by itself. It is not multiplied by any variable. Its value is always, and unequivocally, twelve. It does not fluctuate or change. Therefore, 12 fits the definition of a constant term perfectly. In summary, while 4x, y, and 6z are all variable terms whose values can change, 12 is the only term with a value that is permanently fixed, making it the sole constant in the expression.
