1/2n + 1 = 8
Understand the Problem
The question is asking to solve the equation 1/2n + 1 = 8 for the variable n. This involves isolating n to find its value.
Answer
\( n = 14 \)
Answer for screen readers
The final answer is ( n = 14 ).
Steps to Solve
- Subtract 1 from both sides
To isolate the term with ( n ), subtract 1 from both sides of the equation:
$$ \frac{1}{2}n + 1 - 1 = 8 - 1 $$
This simplifies to:
$$ \frac{1}{2}n = 7 $$
- Multiply both sides by 2
Next, to eliminate the fraction, multiply both sides of the equation by 2:
$$ 2 \times \frac{1}{2}n = 2 \times 7 $$
This simplifies to:
$$ n = 14 $$
The final answer is ( n = 14 ).
More Information
The solution ( n = 14 ) means that when you substitute this value back into the original equation ( \frac{1}{2}n + 1 = 8 ), both sides of the equation will equal 8, confirming that the solution is correct.
Tips
- A common mistake is forgetting to subtract 1 from both sides first, leading to incorrect calculations.
- Another mistake is not multiplying both sides by the same number, which can change the equation.
AI-generated content may contain errors. Please verify critical information
