Compound Inequalities

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'.

Front

What does 'and' mean in a compound inequality?

Back

It means both conditions must be true at the same time.

Front

What does 'or' mean in a compound inequality?

Back

It means at least one of the conditions must be true.

Front

How do you graph 'and' inequalities?

Back

You find the overlap of the solutions on a number line.

Front

How do you graph 'or' inequalities?

Back

You shade the regions that satisfy either inequality on a number line.

Front

What is the solution to the compound inequality x > 2 or x ≤ -3?

Back

The solution includes all numbers greater than 2 and all numbers less than or equal to -3.

Front

What is the solution to the compound inequality x ≥ 2 and x ≤ 4?

Back

The solution includes all numbers from 2 to 4, including 2 and 4.

Front

What is the solution to the compound inequality -4x + 1 ≤ 21 and 5x + 2 < 22?

Back

The solution is x ≥ -5 and x < 4.

Front

What does the graph of 'x > 2 or x ≤ -3' look like?

Back

It has two separate shaded regions: one to the right of 2 and one to the left of -3.

Front

What does the graph of 'x ≥ 2 and x ≤ 4' look like?

Back

It has a single shaded region between 2 and 4, including both endpoints.