Lesson 2.16

Literal Equations (Advanced)

What if the variable you want is stuck in a fraction? Or trapped in two different terms? This is where factoring becomes our secret weapon.

Introduction

Solving is straightforward. But what about ? Here, appears twice, and we can't just "combine like terms" because and are different letters. To get alone, we have to factor it out.

Past Knowledge

The Distributive Property in reverse: .

Today's Goal

Isolate variables when they appear multiple times or are stuck in fractions.

Future Success

Critical for finding inverse functions in Pre-Calculus.

Key Concepts

The Factoring Trick

If you can't combine the terms, factor the variable out.

Problem

Factor Out X

Result

Now divide by the parenthesis group:

Worked Examples

Example 1: Standard Form to Slope-Intercept

Basic

Solve for .

1

Subtract 3x

2

Divide by 2

Divide EVERY term by 2.

Now it's ready to graph!

Example 2: Variables on Both Sides

Intermediate

Solve for .

1

Group X Terms

Subtract to get all on the right.

2

Factor Out X

3

Divide by Parenthesis

Example 3: Stuck in a Denominator

Advanced

Solve for .

This is Ohm's Law for multiple batteries.

1

Clear the Fraction

Multiply both sides by .

2

Distribute and Group

We need all together. Distribute , then move .

3

Factor and Divide

Common Pitfalls

Dividing Before Factoring

In , students might try to divide by . This is illegal if could be zero, and it doesn't isolate anyway (you'd just move it).

Real-Life Applications

Electronics: The formula above () tells an engineer exactly how many battery cells () are needed to achieve a specific current (), given the internal resistance () of each cell. Rearranging allows for "Reverse Engineering" components to fit a design.

Practice Quiz

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