Which expression is equivalent to $17 s-10+3(2 s+1)$?
Answer (1)
Distribute the 3: 17 s − 10 + 3 ( 2 s + 1 ) = 17 s − 10 + 6 s + 3 .
Combine like terms: 17 s + 6 s − 10 + 3 .
Simplify: ( 17 + 6 ) s + ( − 10 + 3 ) = 23 s − 7 .
The equivalent expression is 23 s − 7 .
Explanation
Understanding the Problem We are asked to find an expression equivalent to 17 s − 10 + 3 ( 2 s + 1 ) . This involves distributing the 3 and then combining like terms.
Distributing First, distribute the 3 into the parentheses: 17 s − 10 + 3 ( 2 s + 1 ) = 17 s − 10 + 6 s + 3
Combining Like Terms Next, combine the like terms, which are the terms with s and the constant terms: 17 s + 6 s − 10 + 3
Simplifying Now, simplify the expression by adding the coefficients of s and the constant terms: ( 17 + 6 ) s + ( − 10 + 3 ) = 23 s − 7
Final Answer Therefore, the expression equivalent to 17 s − 10 + 3 ( 2 s + 1 ) is 23 s − 7 .
Examples
Understanding how to simplify algebraic expressions like this is useful in many real-world situations. For example, if you are calculating the total cost of items with a discount and sales tax, you might need to simplify an expression to find the final price. Suppose you are buying 's' number of shirts, each costing $17, and you have a coupon for $10 off. Additionally, there's a special offer where you get 3 sets of (2 shirts plus $1) at the same price. The expression 17 s − 10 + 3 ( 2 s + 1 ) helps you calculate the total cost after applying the coupon and special offer. Simplifying this expression to 23 s − 7 makes it easier to quickly compute the total cost for any number of shirts.
