Algebra I
Compound Inequalities
Lesson
A compound inequalityis two inequalities joined together. The most common kind is the “between” or AND case, which says that is between two values:
This reads “ is greater than AND less than .”
To solve, do the same operation to all three parts at once. Treat the middle as the target you want to isolate.
The same rules from one-step inequalities apply: when you multiply or divide all parts by a negative, you must flip both inequality symbols.
Worked example 1
Subtract 3 from all three parts:
Worked example 2
Divide all three parts by 2 (positive — no flip):
How to type your answer
Write your final answer in the form a<x<b (or with <=). No spaces. Examples: -5<x<4, 2<=x<=5, -1<x<=3.
Practice
Work through these. Stuck? Click Get a hint.
Warm-Up
Quick problems to get going.
Problem 1
Problem 2
Problem 3
Problem 4
Practice
Standard problems matching the lesson.
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Challenge
Harder problems — edge cases, trickier numbers, multiple steps.
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22