Here is a correct phrase that represents the algebraic expression, followed by an explanation.
Correct Phrase: Nine more than the product of three and y.
Explanation
To accurately translate the algebraic expression 3y + 9 into a verbal phrase, it is essential to understand how each component and operation is represented in words. The expression consists of two main parts joined by an addition sign: the term ‘3y’ and the constant ‘9’.
First, let’s analyze the term ‘3y’. In algebra, when a number (a coefficient) is placed directly next to a variable, it implies multiplication. Therefore, ‘3y’ means “3 multiplied by y.” This can be verbalized as “three times y” or, more formally, “the product of three and y.” The letter ‘y’ represents an unknown number, so we are taking a quantity and multiplying it by three.
Next, we consider the ‘+’ symbol, which represents addition. There are many words and phrases used to denote addition, such as “plus,” “added to,” “the sum of,” “increased by,” and “more than.” The expression adds the number nine to the term ‘3y’.
Combining these interpretations, we can construct a complete phrase. We are adding 9 to the quantity “the product of three and y.” This leads to several correct verbal translations. One of the most common and precise phrases is “nine more than the product of three and y.” The phrase “more than” clearly indicates addition. Another perfectly valid description is “the sum of three times y and nine.” Similarly, one could say “the product of three and y, increased by nine.” Each of these phrases accurately captures the two mathematical steps involved: first the multiplication of 3 and y, and second, the addition of 9 to that result.
