Lesson 2.1

One-Step Equations (+/−)

Solving an equation is like unwrapping a gift—you work backwards to reveal the mystery value inside. Start simple by undoing addition and subtraction to get the variable all by itself.

Introduction

The goal of solving any equation is isolation: getting the variable alone on one side of the equals sign (like ). To do this, we use inverse operations—actions that undo each other.

Past Knowledge

You know that addition and subtraction are opposites ($5 - 5 = 0$).

Today's Goal

Solve equations like and .

Future Success

Every advanced equation (quadratics, calculus) eventually boils down to these simple steps.

Key Concepts

The Golden Rule of Equations

Whatever you do to one side, you must do to the other.

This keeps the scale balanced.

1. Undoing Addition

If a number is being added to the variable, subtract it from both sides.

Subtract 4

2. Undoing Subtraction

If a number is being subtracted from the variable, add it to both sides.

Add 7

Worked Examples

Example 1: Undoing Addition

Basic

Solve for :

1

Identify the Operation

15 is added to . Inverse of adding is subtracting.

2

Apply to Both Sides

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Example 2: Negative Numbers

Intermediate

Solve for :

1

Isolate Variable

Add 8 to both sides to cancel out the -8.

2

Calculate

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Example 3: Variable on Right Side

Tricky

Solve for :

1

Don't Panic!

The steps are identical. Focus on the side with the variable.

2

Subtract 9 from Both Sides

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Common Pitfalls

Subtracting from the Wrong Number

In , subtract 5 from 12. Don't subtract 12 from 5!

Ignoring Signs

requires adding 6. If you subtract 6, you'll get , which is wrong. (Check: ).

Real-Life Applications

Every time you check a receipt, you're solving a one-step equation. "My total was $25. The tax was $2. How much was the meal?"

Subtract 2, and you find the meal was $23.

Practice Quiz

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