Question

1. find the error a student solved the equation 6n + 8 = 4n - 9. find his mistake and correct it.

6n+8 = 4n-9
6n+8 - 8 = 4n-9 - 8
6n = 4n-1
6n-4n = 4n-4n-1
2n = -1
n = -0.5

Explanation:

Step1: Identify arithmetic error

When calculating $-9 - 8$, the student incorrectly got $-1$ instead of $-17$.

Step2: Correct the subtraction step

$6n + 8 - 8 = 4n - 9 - 8$ simplifies to $6n = 4n - 17$

Step3: Isolate variable terms

Subtract $4n$ from both sides:
$6n - 4n = 4n - 4n - 17$
$2n = -17$

Step4: Solve for $n$

Divide both sides by 2:
$n = \frac{-17}{2}$

Answer:

The student's mistake was miscalculating $-9 - 8$ as $-1$ (it should be $-17$). The correct solution is $n = -\frac{17}{2}$ or $n = -8.5$