Lesson 2.15

Literal Equations (Basic)

A "literal" equation is just an equation with mostly letters. You use the exact same moves to solve as you do to solve .

Introduction

"Solve for " just means "get by itself." It doesn't matter if the other side is a number like 10 or a mess of letters like . The logic is identical.

Past Knowledge

Inverse operations (undo adding with subtracting, multiplying with division).

Today's Goal

Rearrange formulas to highlight a specific variable.

Future Success

You will do this constantly in Physics () and Linear Equations ().

Key Concepts

Rearranging Furniture

Think of specific variables as pieces of furniture. "Solve for " means moving everything else to the other room.

Standard Equation

Subtract 5, Divide by 2

Literal Equation

Subtract b, Divide by a

The STEPS are the same. The ANSWER just looks weirder.

Worked Examples

Example 1: One-Step Formula

Basic

Solve for .

This is the Distance Formula (Distance = Rate x Time).

1

Identify the Operation

is multiplied by . To undo multiplication, we divide.

Example 2: Two-Step Linear

Intermediate

Solve for .

1

Move the Constant ()

Subtract from both sides.

2

Divide by Coefficient ()

Solved!

Example 3: Perimeter Formula

Advanced

Solve for .

1

Subtract 2W

2

Divide by 2

Divide the ENTIRE left side by 2.

Common Pitfalls

Bad Cancellation

In , you cannot just cancel the 2s to get . You must divide BOTH parts of the numerator.

Case Sensitivity

Capital (Perimeter) is not the same as lowercase (pressure). Keep your variable cases consistent!

Real-Life Applications

International Travel: The US uses Fahrenheit, but Europe uses Celsius. The formula is . If you're in Paris and see 20°C, that's easy. But if you know it's 70°F and want to know Celsius, you need to rearrange the formula first: .

Practice Quiz

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