$10n + 16 = 6n +
Answer (2)
To solve the equation 10 n + 16 = 6 n + c , we isolate n by rearranging the equation and simplifying it. After manipulating the equation, we find that n is expressed as n = 4 c − 16 . This solution depends on the specific value of c .
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Rearrange the equation 10 n + 16 = 6 n + c to isolate terms with n on one side.
Simplify the equation to 4 n = c − 16 .
Divide both sides by 4 to solve for n : n = 4 c − 16 .
The solution for n depends on the value of c : n = 4 c − 16 .
Explanation
Understanding the Equation Let's analyze the given equation: 10 n + 16 = 6 n + ... . The equation is incomplete, and we need to solve for n . To do this, we need to add a constant term to the right side of the equation. Let's call this constant c . So, the equation becomes 10 n + 16 = 6 n + c .
Isolating the Variable Now, we need to rearrange the equation to isolate the terms with n on one side and the constant terms on the other side. We can subtract 6 n from both sides of the equation: 10 n − 6 n + 16 = 6 n − 6 n + c , which simplifies to 4 n + 16 = c . Next, we subtract 16 from both sides: 4 n + 16 − 16 = c − 16 , which simplifies to 4 n = c − 16 .
Solving for n To solve for n , we divide both sides of the equation by 4: 4 4 n = 4 c − 16 , which gives us n = 4 c − 16 . This is the general solution for n in terms of c .
Final Solution in Terms of c Since the original equation is incomplete, we cannot find a unique numerical value for n . The solution for n depends on the value of c . Without knowing the value of c , we can only express n in terms of c : n = 4 c − 16 .
Examples
This type of problem, solving for a variable in a linear equation, is useful in many real-world situations. For example, imagine you are calculating the cost of a service. The total cost might be represented as 10 n + 16 , where n is the number of hours of service and 16 is a fixed fee. If you know that another service costs 6 n + c and you want to find the number of hours ( n ) for which the costs are equal, you would solve the equation 10 n + 16 = 6 n + c . This helps in comparing prices and making informed decisions.
