Lesson 1: Inequalities

What is an Algebraic Inequality?
what is a solution?
How can you use Interval Notation to graphically show your solution?

Create and graph equations or inequalities to describe numbers or relationships.

Lesson Description: This lesson introduces the fundamental symbols and logic of linear inequalities. Students will learn to read, write, and interpret inequality statements (<, >, <=, >=). The curriculum covers:
Graphing solutions on a number line using open and closed circles (or parentheses and brackets). Interval Notation, a standard shorthand for describing sets of numbers. The Addition and Subtraction Properties of Inequality, which mirror those of equations. The critical Reversal Rule: Multiplying or dividing by a negative number flips the inequality symbol.
Purpose: The purpose of Section 4.1 is to move students from "point solutions" (where x = 5) to "set solutions" (where x > 5). This conceptual shift is vital for understanding real-world constraints—such as budgets, speed limits, or safety thresholds—where there isn't just one right answer, but a "zone" of valid answers. Mastering the negative-flip rule here prevents the most common errors in later algebra and calculus courses.
Depth of Knowledge (DOK)
DOK Level 1 & 2
Level 1 (Recall): Recognizing inequality symbols and correctly identifying which direction to shade on a number line.
Level 2 (Skill/Concept): Solving one-step inequalities and applying the "negative flip" rule. Students must also translate between three different representations: the algebraic inequality, the visual graph, and the formal interval notation.

class work and online work

"you try" on page 102 along with practice problems