Expand and simplify $3(6 c-4)+7 c$
Answer (1)
Distribute the 3: 3 ( 6 c − 4 ) = 18 c − 12 .
Rewrite the expression: 18 c − 12 + 7 c .
Combine like terms: 18 c + 7 c = 25 c .
The simplified expression is 25 c − 12 .
Explanation
Understanding the Problem We are given the expression 3 ( 6 c − 4 ) + 7 c and our goal is to expand and simplify it. This involves distributing the 3 across the terms inside the parentheses and then combining like terms.
Distributing the Constant First, we distribute the 3 to both terms inside the parentheses: 3 ( 6 c − 4 ) = 3 × 6 c − 3 × 4 = 18 c − 12 So, the expression becomes: 18 c − 12 + 7 c
Combining Like Terms Next, we combine the like terms, which are the terms containing c :
18 c + 7 c = 25 c So, the expression simplifies to: 25 c − 12
Final Answer Therefore, the expanded and simplified form of the given expression is 25 c − 12 .
Examples
Imagine you are buying multiple items at a store. You want to buy 6 items that cost 'c' dollars each, but you have a coupon that gives you a $4 discount on each of those items. Additionally, you need to buy 7 more items that cost 'c' dollars each. The expression 3 ( 6 c − 4 ) + 7 c can represent the total cost. Expanding and simplifying this expression helps you easily calculate the total cost: 25 c − 12 . If each item costs $2 (c=2), the total cost would be $25 \times 2 - 12 = 50 - 12 = $38.
