8>7n+1

7>7n
1>n
n<1

8>7n+1

8-1>7n+1-1
7>7n
1>n

* You do not change the sign because you did not divide by a negative. You only change the sign when you do divide by a negative number.

To solve the inequality 8 > 7n + 1, we need to isolate the variable n on one side of the equation.

Step 1: Subtract 1 from both sides of the inequality:
8 - 1 > 7n + 1 - 1
7 > 7n

Step 2: Divide both sides of the inequality by 7:
7/7 > (7/7)n
1 > n

Therefore, the solution to the inequality 8 > 7n + 1 is n < 1.