Understanding Inequalities
An inequality is a mathematical statement that compares two expressions using inequality symbols (<, >, ≤, ≥). Unlike equations, inequalities have a range of solutions.
Key Rules
- Add or subtract the same number from both sides
- Multiply or divide both sides by a positive number
- When multiplying or dividing by a negative number, flip the inequality sign
Important Concepts:
- Solutions are ranges of numbers, not single values
- The inequality sign flips when multiplying or dividing by a negative number
- Check solutions by testing numbers in the solution range
Solving Process
- 1
Isolate Variable Terms
Move all terms with the variable to one side.
- 2
Isolate Constants
Move all constant terms to the other side.
- 3
Solve for the Variable
Divide or multiply to isolate the variable (watch for sign flips).
- 4
Check Solution
Test a number in your solution range.