Lesson 2: Solving Linear Inequalities

What does a solution to an equation mean graphically?
How can you show the solution set?

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

Lesson Description This lesson combines the multi-step solving strategies from Section 3.3 with the unique constraints of inequalities from Section 4.1. Students will apply the Distributive Property, combine like terms, and move variables to one side to isolate the solution set. The core focus remains on maintaining the "balance" of the inequality while strictly adhering to the rule of flipping the inequality symbol when multiplying or dividing by a negative number. Students are expected to express their final answers in three formats:
Algebraic inequality (e.g., x >= -3) Graphical representation on a number line Interval notation (e.g., [-3, infinity))
Purpose: The purpose of Section 4.2 is to achieve computational precision within a more complex logical framework. While the steps are nearly identical to solving linear equations, inequalities require a higher level of "sign awareness." This section trains students to anticipate when a solution set will "flip" directions, a skill that is essential for understanding domains, ranges, and optimization problems in higher-level math and science courses.
Depth of Knowledge (DOK) Level DOK Level 2 & 3
Level 2 (Skills and Concepts): Executing a multi-step procedure to solve for $x$. This involves coordinating multiple algebraic rules (distribution, inverse operations, and sign changes) and translating that result into a visual graph.
Level 3 (Strategic Thinking): Comparing and contrasting the solution process of an equation versus an inequality. Students must justify why a symbol was flipped and check the validity of their solution set by testing "test points" within their shaded region to ensure the original inequality holds true.

Classwork and online work

"you try' page 104 as well as practice problems