Lesson 3.9

Solving "OR" Inequalities

Two separate problems, one shared graph. Unlike "AND", these inequalities don't have to agree on anything. They just share the same number line.

Introduction

In an "OR" inequality, can satisfy the left condition OR the right condition. Solving them is straightforward: treat them as two completely separate math problems, then graph both answers.

Past Knowledge

Lesson 3.8 ("AND" inequalities) and Lesson 3.7 (Intro to Compound).

Today's Goal

Solve and graph disjoint "OR" inequalities (The "Wings").

Future Success

This logic is used for Absolute Value Greater Than problems (Lesson 3.11).

Key Concepts

Divide and Conquer

Draw a line down the middle. Solve the left. Solve the right. They never interact until the very end when you graph them.

Problem A

Divide by 2

Problem B

Add 5

Final Answer:

Worked Examples

Example 1: Basic Disjoint

Basic

Solve .

1

Solve Left

Subtract 4.

2

Solve Right

Add 3.

Answer:

Example 2: Multi-Step

Intermediate

Solve .

1

Solve Left

Subtract 1
Divide by 2
2

Solve Right

Add 2
Divide by 3
Answer:

Example 3: All Real Numbers?

Advanced

Solve .

1

Graph it mentally

  • One ray goes left from 5 (covers 4, 3, 2, 1, 0, -1...).
  • One ray goes right from 0 (covers 1, 2, 3, 4, 5, 6...).
2

Conclusion

Every single number on the number line is covered by at least one arrow. The solution is All Real Numbers.

Common Pitfalls

The "Impossible" Intersection

Students confuse AND/OR. is Impossible (No Solution). But is a perfectly valid graph (Two Wings).

Real-Life Applications

Discounts: "Kids under 12 OR Seniors over 65 get a discount."

. If your age is 30, you fail both checks. If you are 70, you pass one check, so you get the discount.

Practice Quiz

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