Introduction to Inequalities
An inequality compares two expressions using inequality symbols. Unlike equations, inequalities often have infinitely many solutions, which can be shown on a number line.
What You Need to Know
Key Concept Diagram
Inequality symbols: < (less than), > (greater than), <= (less than or equal), >= (greater than or equal)
Solve inequalities like equations, but flip the sign when multiplying or dividing by a negative number
The solution to an inequality can be graphed on a number line using open circles (strict) or closed circles (includes the endpoint)
Inequalities model real-world constraints, such as speed limits and age restrictions
Key Vocabulary
Inequality
A mathematical statement comparing two expressions using <, >, <=, or >=
Solution set
All the values of the variable that make the inequality true
Open circle
Used on a number line to show a value is NOT included (strict inequality)
Closed circle
Used on a number line to show a value IS included (non-strict inequality)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Which values satisfy the inequality x > 3?
Question 2
Solve: 2x < 10
Question 3
Solve: −3x >= 12
Key Concepts Summary
- ●Inequality symbols: < (less than), > (greater than), <= (less than or equal), >= (greater than or equal)
- ●Solve inequalities like equations, but flip the sign when multiplying or dividing by a negative number
- ●The solution to an inequality can be graphed on a number line using open circles (strict) or closed circles (includes the endpoint)
- ●Inequalities model real-world constraints, such as speed limits and age restrictions