What is the key difference between solving an 'or' compound inequality and an 'and' compound inequality?

For 'or', only one inequality needs to be true; for 'and', both inequalities must be true at the same time.

Which of the following represents the graph of x > 2 OR x < -1?

A number line with an open circle at -1, shading to the left, and an open circle at 2, shading to the right.

I can solve simple and compound inequalities and graph the solutions on a number line.

1
A compound inequality combines two simple inequalities with the words "and" or "or."
2
With an "or" compound inequality, only one of the inequalities has to be true, but with an "and" compound inequality, both inequalities must be true at the same time.
3
When graphing an "and" compound inequality, the solution is where the two plots overlap, meaning both inequalities are true in that range.