Write an expression for 7 less than y
The Correct Answer and Explanation is:
The expression for “7 less than y” can be written as:
[
y – 7
]
Explanation:
When we see a phrase like “7 less than y,” it means we are taking the value of ( y ) and subtracting 7 from it. In math, “less than” usually indicates subtraction, and whatever number comes before “less than” is subtracted from the variable or value that comes after. So, “7 less than y” translates directly to ( y – 7 ).
To further understand this, let’s break down the phrase:
- Identify the Variable: Here, ( y ) is our variable. A variable is a symbol, often a letter, that represents a number or value that can change. In this case, ( y ) could be any number, depending on the context.
- Understand “Less Than”: In everyday language, “less than” refers to reducing a certain amount from a given number. Mathematically, it means we will perform a subtraction operation. When we say “7 less than y,” it means we start with ( y ) and then reduce or subtract 7 from it.
- Construct the Expression: Now that we know “7 less than y” means taking ( y ) and subtracting 7, we write this as ( y – 7 ).
- Examples for Clarity: To illustrate, if ( y ) is 10, then “7 less than ( y )” would be ( 10 – 7 = 3 ). If ( y ) is 20, then “7 less than ( y )” would be ( 20 – 7 = 13 ).
Why Order Matters:
It’s essential to write the expression correctly, as order matters in subtraction. “7 less than y” should not be confused with “y less than 7,” which would be written as ( 7 – y ). These two expressions are not equivalent. In ( y – 7 ), we start with ( y ) and reduce by 7, but in ( 7 – y ), we start with 7 and reduce by ( y ).
In summary, the expression ( y – 7 ) accurately captures “7 less than y” because we start with ( y ) and subtract 7. This approach to translating verbal statements into algebraic expressions is a common and valuable skill in mathematics.