Definition: A compound inequality joins two inequalities with and or or; an and statement describes an overlap of solutions, an or statement describes a union.
What are the two types?
With and, both conditions must hold at once, as in 2 < x ≤ 9. The graph is a segment between the two numbers. With or, at least one condition holds, as in x < -1 or x ≥ 4. The graph has two rays pointing away from each other.
How do you solve one?
Treat each inequality separately, or work on all three parts of a chain at once. Reverse the inequality sign whenever you multiply or divide by a negative number.
Example. Solve -7 < 3 – 2x ≤ 11. Subtract 3 from every part: -10 < -2x ≤ 8. Divide by -2 and flip both signs: 5 > x ≥ -4, which is -4 ≤ x < 5.
What mistakes occur?
Forgetting to flip the signs, and then writing the chain in the wrong order, such as 5 < x < -4, which is impossible. Also, not every and statement has a solution: x > 8 and x < 3 share no numbers. Absolute value inequalities turn into compound inequalities too.