Lesson 9: Introduction to Inequalities
An inequality compares two expressions using symbols that show whether one value is less than, greater than, or possibly equal to another.
Common Inequality Symbols
- < — "less than" (e.g.,
3 < 7) - > — "greater than" (e.g.,
10 > 4) - ≤ — "less than or equal to" (e.g.,
x ≤ 5) - ≥ — "greater than or equal to" (e.g.,
y ≥ 2)
Graphing Inequalities on a Number Line
When graphing on a number line:
- Use an open circle if the endpoint is not included (symbols
<or>). - Use a closed circle (filled) if the endpoint is included (symbols
≤or≥). - Shade to the right for "greater than" and to the left for "less than".
Example: \(x > 2\)
Number line from -2 to 6 with an open circle at 2 and a shaded ray to the right indicating all numbers greater than 2.
Example: \(x \le 4\)
Number line from -2 to 6 with a closed circle at 4 and a shaded ray to the left indicating all numbers less than or equal to 4.
Practice Problems
- Write an inequality showing “5 is less than 9.â€
- Graph the inequality
x ≤ 4on a number line (use open/closed circle correctly). - True or False:
7 ≥ 10. - Which inequality symbol completes this sentence:
12 ___ 12?
Lesson Summary
Inequalities use <, >, ≤, and ≥ to compare values.
Use open circles for strict inequalities (<, >) and closed circles for inclusive inequalities (≤, ≥).
Shade to the right for "greater than" and to the left for "less than."