1. Writing and Graphing Inequalities Because “I<3U” does not mean “I love you.” Mathematically, it means I less than 3 of you.

2. What is an inequality? Mathematical sentence that compares quantities. To solve an inequality, you have to find all values for the variable that make the sentence true. Inequalities do not contain equal signs.

3. Some Common Phrases in Inequality Statements Symbols<>≤≥≠ Words less than fewer than smaller than below greater than more than Exceeds larger than above less than or equal to no more than at most Maximum not greater than greater than or equal to no less than at least Minimum Not smaller than does not equal

4. Translating sentences to inequalities Example 1: A number is less than 2. Since we don’t know what the number is, we will use x to represent the unknown number. x < 2 Example 2: The cost of the shirt exceeds $15. x > 15 Exceeds means “is greater than.”

5. Example 3: The maximum number of students in the class is 28. Example 4: The weight of the package was no less than 50 pounds. x ≤ 28 x ≥ 50 Maximum means that there could be 28 students or less in the class. If something is no less than 50, it could be greater than or equal to 50.

6. To graph an inequality on a number line: – Draw a number line, and mark the critical point near the center of the number line. – Frame the critical point by filling in a number to the left and the right. – Put a circle on the critical point. Shade in the circle for inequality symbols ≥ and ≤. Leave the circle open (unshaded) for inequality symbols >, <, and ≠. – Draw a shaded arrow towards the part of the number line that makes the inequality statement true.

7. Examples of Graphing Inequalities Example 1: x > 2 Example 2: x < -6 2 13 -6 -7-5

8. Example 3: x ≤ 28 Example 4: x ≥ -4 28 27 29 -4 -5-3