Lesson 2.18
Isolating the Absolute Value
Before you can see what's inside the box, you have to get the box by itself. Absolute value bars act like an impenetrable shield—you cannot touch the inside until the outside is clear.
Introduction
In , the is trapped. You cannot distribute the 2. You cannot subtract the 3. You must treating the entire group as a single variable (like a box) and isolate it first.
Past Knowledge
Solving two-step equations (undo addition, then multiplication).
Today's Goal
Isolate the absolute value bars on one side of the equation.
Future Success
This is the first step to solving absolute value equations.
Key Concepts
Treat the Bars like a Box
Imagine is a solid box. You can move things around it, but you cannot reach inside it.
Problem
Result
Worked Examples
Example 1: Undo Addition
BasicIsolate the absolute value in .
Subtract 7
Example 2: Undo Multiplication
IntermediateIsolate the absolute value in .
Divide by -3
Do NOT distribute the -3 inside.
Example 3: Two-Step Isolation
AdvancedIsolate the absolute value in .
Add 4
Multiply by 3
Common Pitfalls
Distributing Into Bars
This is the #1 mistake. IS NOT . The bars are a wall. You cannot distribute across them.
Stopping Too Early
In , students often try to "split" it immediately. You MUST get rid of the +5 first, or your answers will be wrong.
Real-Life Applications
Package Opening: You can't assemble a bookshelf until you unpack the box. Isolating the variable group is like removing the packaging—it's a necessary step before you can access the components inside.
Practice Quiz
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