Graphing and Solving Inequalities
This page introduces the fundamental concepts of inequalities, their symbols, and how to graph them on a number line. It covers essential information for students learning to solve inequalities with multiplication and division.
The page begins by presenting the four main inequality symbols:
- Greater than (>)
- Less than (<)
- Greater than or equal to (≥)
- Less than or equal to (≤)
Vocabulary: Inequality symbols are mathematical symbols used to show the relationship between two expressions that are not equal.
The document then explains how to graph inequalities on a number line, emphasizing the difference between open and closed circles:
Highlight: Open circles (○) are used for strict inequalities (> or <), while closed circles (●) represent inequalities that include equality (≥ or ≤).
Several examples of graphing inequalities are provided, such as x > 0 and x > -2, to illustrate the correct use of open and closed circles on a number line.
The page then delves into solving one-step inequalities, covering addition, subtraction, multiplication, and division. It emphasizes a crucial rule when solving inequalities:
Definition: When multiplying or dividing an inequality by a negative number, the inequality sign must be flipped.
This rule is particularly important for solving inequalities using multiplication and division. The document provides examples to demonstrate this concept, such as:
Example: -7x > 63
Dividing both sides by -7 (a negative number), we flip the sign:
x < -9
The page concludes with a note on solving inequalities with addition and subtraction, stating that the inequality sign does not change in these operations unless adding a negative number, which is equivalent to subtraction.
