Solve the equation:
\[\frac{1}{3}(n+1) = \frac{1}{6}(3n-5)\]
Provide a step-by-step solution.
Answer (3)
1/3(n+1)=1/6(3n-5) 1/3n+1/3 = 1/2n-5/6 1/3 = 1/6n - 5/6 7/6 = 1/6n so n = (7/6) / (1/6) n = 7
Consider the equation 3 1 ( n + 1 ) = 6 1 ( 3 n − 5 ) .
**1 step. **Multiply this equation by 6:
3 6 ( n + 1 ) = 6 6 ( 3 n − 5 ) , 2 ( n + 1 ) = 3 n − 5 , 2 n + 2 = 3 n − 5.
**2 step. **Separate expressions in such way, that variables are in the left side and the numbers are in the right side:
2 n − 3 n = − 5 − 2.
3 step. Add expressions in both sides:
n ⋅ ( 2 − 3 ) = − ( 5 + 2 ) , − 1 ⋅ n = − 7 , − n = − 7.
4 step. Multiply this equaiton by -1:
n=7.
Answer: n=7.
The solution to the equation 3 1 ( n + 1 ) = 6 1 ( 3 n − 5 ) is n = 7 . This was found by eliminating fractions, distributing, and rearranging the equation to isolate n . The final answer is n = 7 .
;
