Solve for $n$. $11(n-1)+35=3n$
Answer (2)
Distribute: 11 ( n − 1 ) + 35 = 11 n − 11 + 35 .
Combine constants: 11 n + 24 = 3 n .
Isolate n : 8 n = − 24 .
Solve for n : n = − 3 . The solution is − 3 .
Explanation
Problem Analysis We are given the equation 11 ( n − 1 ) + 35 = 3 n and asked to solve for n . We will simplify and isolate n to find the solution.
Distribute First, distribute the 11 on the left side of the equation: 11 ( n − 1 ) + 35 = 11 n − 11 + 35 = 3 n
Combine Constants Next, combine the constants on the left side: 11 n − 11 + 35 = 11 n + 24 = 3 n
Subtract 3n Now, subtract 3 n from both sides of the equation to get the terms with n on one side: 11 n + 24 − 3 n = 3 n − 3 n
8 n + 24 = 0
Subtract 24 Subtract 24 from both sides of the equation to isolate the term with n : 8 n + 24 − 24 = 0 − 24
8 n = − 24
Divide by 8 Finally, divide both sides by 8 to solve for n : 8 8 n = 8 − 24
n = − 3
Final Answer Therefore, the solution to the equation 11 ( n − 1 ) + 35 = 3 n is n = − 3 .
Examples
In real-world scenarios, solving linear equations like this can help determine the break-even point in business. For example, if n represents the number of units you need to sell, the equation could represent the point where your revenue equals your costs. Solving for n tells you how many units you need to sell to break even. Understanding how to manipulate and solve these equations is crucial for making informed financial decisions.
To solve the equation 11 ( n − 1 ) + 35 = 3 n , first distribute and combine like terms. After isolating n , we find that n = − 3 .
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