Solve the inequality and give the interval notation

|7 - x| >= 1

When solving for x inside an absolute value, you can set up two equations. One for the positive and one for the negative(since we’re dealing with absolutes.

We end up with:
7 - x >= 1
7 - x <= -1 (inequalities’ signs flip when multiplying or dividing by a negative.)

7 - x >= 1
7 - 1 >= x
X <= 6

7 - x <= -1
7 + 1 <= x
X>= 8

X: (-infinity, 6]U[8, infinity)