-4x-1>31

To solve the inequality -4x - 1 > 31, we can start by isolating the variable x.

First, add 1 to both sides of the inequality:
-4x - 1 + 1 > 31 + 1
-4x > 32

Next, divide both sides of the inequality by -4. It's important to remember that whenever we multiply or divide an inequality by a negative number, we must flip the direction of the inequality.
-4x / -4 < 32 / -4
x < -8

Therefore, the inequality -4x - 1 > 31 is true for any x value less than -8.