📖Definition
An inequality is a mathematical statement that compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Unlike equations which have one solution, inequalities often have a range of solutions.
📐Formula
x > 5 means x can be any number greater than 5. x ≤ 3 means x can be 3 or any number less than 3. The solution is usually shown on a number line or in interval notation.
📝Step-by-Step Guide
Isolate the Variable
Use the same steps as solving equations: add, subtract, multiply, or divide both sides.
Flip the Sign When Multiplying/Dividing by Negative
When you multiply or divide both sides by a negative number, reverse the inequality sign.
Graph on a Number Line
Open circle (○) for < or >, closed circle (●) for ≤ or ≥. Shade the direction of solutions.
Write in Interval Notation
Use parentheses for < or > and brackets for ≤ or ≥.
⚠️Common Mistakes to Avoid
- Forgetting to flip the inequality sign when dividing by a negative
- Using a closed circle when it should be open (or vice versa)
- Confusing < with >
- Not checking the solution with test values
- Incorrectly combining compound inequalities
✏️Practice Problems
Solve x + 4 > 7
Answer: x > 3
Solve -3x ≤ 12
💡 Hint: Remember to flip the sign when dividing by -3
Answer: x ≥ -4
Solve 2(x - 1) < 3x + 5
Answer: x > -7
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