Solving Inequalities
Inequalities describe ranges of values rather than a single solution. Solving them is similar to solving equations, but with one important difference: multiplying or dividing by a negative number flips the inequality sign.
What You Need to Know
Key Concept Diagram
Inequality symbols: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to)
Solve like an equation using inverse operations, but flip the sign when multiplying or dividing by a negative
Graph solutions on a number line: open circle for strict inequalities, closed circle for equal
The solution set of an inequality contains infinitely many values
Key Vocabulary
Inequality
A mathematical statement comparing two expressions using < > <= >=
Solution set
All values that satisfy an inequality
Number line
A visual representation used to show the solution of an inequality
Strict inequality
An inequality using < or > (not including the boundary value)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Solve: 2x + 3 > 11
Question 2
Solve: -3x <= 12
Question 3
On a number line, how is the solution x > 5 represented?
Key Concepts Summary
- ●Inequality symbols: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to)
- ●Solve like an equation using inverse operations, but flip the sign when multiplying or dividing by a negative
- ●Graph solutions on a number line: open circle for strict inequalities, closed circle for equal
- ●The solution set of an inequality contains infinitely many values