Simplify by combining like terms.
(42.) $3-8(7-5 n)$
Answer (2)
To simplify the expression 3 − 8 ( 7 − 5 n ) , first distribute the -8 to get 3 − 56 + 40 n . Then, combine the constants to arrive at the final simplified expression of 40 n − 53 .
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Distribute the -8 across the terms inside the parentheses: 3 − 8 ( 7 ) − 8 ( − 5 n ) = 3 − 56 + 40 n .
Combine the constant terms: 3 − 56 = − 53 .
Rewrite the expression: − 53 + 40 n .
The simplified expression is: 40 n − 53 .
Explanation
Understanding the Problem We are asked to simplify the expression 3 − 8 ( 7 − 5 n ) by combining like terms. This involves distributing the − 8 across the terms inside the parentheses and then combining any constant terms.
Distributing the -8 First, distribute the − 8 to both terms inside the parentheses: 3 − 8 ( 7 ) − 8 ( − 5 n ) 3 − 56 + 40 n
Combining Constant Terms Next, combine the constant terms 3 and − 56 :
3 − 56 = − 53 So the expression becomes: − 53 + 40 n
Final Simplified Expression Finally, we can rewrite the expression with the term containing the variable first: 40 n − 53
Examples
Simplifying expressions is a fundamental skill in algebra. For example, if you are calculating the total cost of buying multiple items with a discount, you might need to simplify an expression like this. Suppose you want to buy 8 items that each cost 7 dollars, but you have a coupon that gives you a discount of 5 dollars per item. The total cost can be represented as 3 + 8 ( 7 − 5 ) , where the 3 represents a fixed shipping cost. Simplifying this expression helps you quickly find the total cost.
