What are Inequalities?
- The "less than" symbol (<), implying one number is smaller than another: 2 < 3
- The "greater than" symbol (>), indicating one number is larger than another: 5 > 2
- The "less than or equal to" symbol (≤), stating that a number could be either smaller than or equal to another number. For instance, 4x ≤ 4 means that x could be an integer value like 4, 3, 2 and so on.
- The "greater than or equal to" symbol (≥), suggesting that the number is either greater than or precisely equal to another number. An example would be x ≥ 6, where x could be 6, 7, 8, or any other number greater than 6.
Methods to solve inequalities
- Linear Inequalities: Represented usually as ax + b < c or ax + b > c
- Quadratic Inequalities: Often in the form ax2 + bx + c < 0 or ax2 + bx + c > 0
- Rational Inequalities: These involve expressions like a/x > b.
- Polynomial Inequalities: A more generalized form that includes higher-degree polynomial functions
- Absolute Value Inequalities: In these, the absolute value of a variable is compared to a number, such as ∣x+3∣<5
What is the solution set for the linear inequality 2x - 3 < 5?
What is the solution set for the quadratic inequality x2 - 4 < 0?
What is the solution set for the rational inequality x/x-1 > 1?
What is the solution set for x3 - x2 < 0?