The Correct Answer and Explanation is:
The correct answer is B. -5x + 12.
To understand why this is the correct choice, we need to look at the components of the original algebraic expression, which is 12 – 5x. An algebraic expression is made up of terms, which are the parts separated by addition or subtraction signs. In this case, the two terms are 12 and -5x. It is very important to recognize that the subtraction sign in front of the 5x makes it a negative term. So, we can think of the expression as a positive 12 being added to a negative 5x, or (+12) + (-5x).
In mathematics, the commutative property of addition states that the order in which you add two terms does not change the result. For example, 3 + 4 is the same as 4 + 3. We can apply this same principle to our algebraic expression. We can swap the order of the two terms, +12 and -5x, without changing the value of the expression.
If we rearrange 12 – 5x by putting the -5x term first, followed by the +12 term, we get -5x + 12. This new expression is mathematically identical to the original one; it is simply written in a different order. This matches option B perfectly.
Let’s quickly review the other options to see why they are incorrect.
Option A, -12x + 5, incorrectly swaps the numbers. The number 12 is the constant term, and 5 is the coefficient of x, not the other way around.
Option C, 5x – 12, has the wrong signs for both terms. It has a positive 5x and a negative 12, whereas the original expression has a negative 5x and a positive 12.
Option D, 12x – 5, also incorrectly assigns the numbers to the variable and the constant term.
