What value of x makes the equation 5(n + 2) = 5 + 6n true?
Understand the Problem
The question is asking for the value of x that makes the given equation true. We need to solve the equation for the unknown variable.
Answer
The value of $n$ that makes the equation true is $n = 5$.
Answer for screen readers
The value of $n$ that makes the equation true is $n = 5$.
Steps to Solve
-
Distribute on the left side
Distribute the 5 across the terms inside the parentheses:
$$ 5(n + 2) = 5n + 10 $$
So the equation becomes:
$$ 5n + 10 = 5 + 6n $$ -
Move variables to one side
Subtract $5n$ from both sides to isolate the variable terms on one side:
$$ 10 = 5 + 6n - 5n $$
This simplifies to:
$$ 10 = 5 + n $$ -
Isolate the variable
Subtract 5 from both sides to solve for $n$:
$$ 10 - 5 = n $$
This simplifies to:
$$ n = 5 $$
The value of $n$ that makes the equation true is $n = 5$.
More Information
This equation illustrates the fundamental properties of algebra, such as the distributive property and the process of isolating variables to find their values. This technique is commonly used to solve linear equations.
Tips
- Forgetting to distribute properly can lead to incorrect results.
- Failing to combine like terms when moving terms from one side of the equation to the other.
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