What is a linear inequation? A linear inequation is a mathematical statement that compares two linear expressions using inequality symbols. The solution of a linear inequation is the set of all values of the variable that satisfy the inequality.
Inequality symbols and their meanings:
| Symbol | Meaning | Example |
|---|---|---|
| < | less than | x < 5 |
| > | greater than | x > 5 |
| ≤ | less than or equal to | x ≤ 5 |
| ≥ | greater than or equal to | x ≥ 5 |
Rules for solving linear inequations:
- Adding or subtracting the same number from both sides does NOT change the inequality
- Multiplying or dividing both sides by a positive number does NOT change the inequality
- Multiplying or dividing both sides by a negative number REVERSES the inequality sign
Important: When you multiply or divide by a negative number, flip the inequality sign!
Example: −2x < 6 → Divide by −2 (negative!) → x > −3 (sign flips from < to >)
Real-life analogy: Think of an inequation like a see-saw. Adding weight to both sides keeps the balance (same direction). But if you multiply by a negative, it's like flipping the see-saw upside down — everything reverses!