Which algebraic expression represents this word description?
The product of seven and the difference between a number and ten
A. $7 x-10$
B. $7(10-x)$
C. $7(x-10)$
D. $10-7 x$
Answer (1)
Represent the unknown number with the variable x .
Express the difference between the number and ten as ( x − 10 ) .
Multiply the difference by seven to get the product: 7 ( x − 10 ) .
The algebraic expression representing the word description is 7 ( x − 10 ) .
Explanation
Understanding the Problem Let's break down the word description to form an algebraic expression. The description is 'The product of seven and the difference between a number and ten'. We'll use 'x' to represent the unknown number.
Finding the Difference First, we need to find the difference between the number and ten. This can be written as x − 10 .
Finding the Product Next, we need to find the product of seven and this difference. This means we multiply 7 by ( x − 10 ) , which gives us 7 ( x − 10 ) .
Matching the Expression Now, we compare our expression 7 ( x − 10 ) with the given options:
A. 7 x − 10 B. 7 ( 10 − x ) C. 7 ( x − 10 ) D. 10 − 7 x
Our expression matches option C.
Final Answer Therefore, the algebraic expression that represents the word description is 7 ( x − 10 ) .
Examples
Algebraic expressions are used in various real-life scenarios. For instance, if you are buying multiple items at a store, you can use an algebraic expression to calculate the total cost. If each item costs 'x' dollars and you buy 7 of them, and you have a coupon for $10 off, the total cost can be represented as 7 ( x − 10 ) . This helps in quickly determining the amount you need to pay.
