Linear inequalities

Definition

Linear inequalities are algebraic expressions involving a linear function where the values are not equal but rather greater than or less than each other. They can be represented on a number line or through interval notation.

5 Must Know Facts For Your Next Test

1. Linear inequalities use symbols like >, <, ≥, and ≤ to compare values.
2. Solving linear inequalities involves similar steps as solving linear equations but requires careful handling of inequality signs.
3. When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.
4. The solution set for a linear inequality in one variable is often an interval or a union of intervals on the number line.
5. Graphing the solution involves shading regions on the number line that satisfy the inequality.

Review Questions

• What happens to the inequality sign when you multiply or divide both sides by a negative number?
• How do you represent the solution set for x > 3 on a number line?
• Can you solve and graph the inequality 2x - 4 ≤ 6?

Related terms

Linear Equation: An algebraic equation in which each term is either a constant or the product of a constant and a single variable.

Interval Notation: A way of writing subsets of the real number line using intervals to show where solutions lie.

Number Line: A visual representation of numbers placed in order on a straight horizontal line.