Lesson 3.3

Solving Inequalities (+/-)

Good news: Solving is exactly like solving . The balance scale still works.

Introduction

If you have less money than your friend, and you both find $10, you still have less money than your friend. Adding or subtracting the same amount from both sides does not change the order.

Past Knowledge

Solving one-step equations (Lesson 2.1).

Today's Goal

Use inverse operations to isolate the variable in inequalities.

Future Success

The only tricky part comes next lesson (multiplication). Master +/- first.

Key Concepts

The Rule of Balance

You can add or subtract any number from both sides, and the inequality symbol stays exactly the same.

Original

Add 5 to both sides

STILL TRUE

Worked Examples

Example 1: Undoing Subtraction

Basic

Solve .

Isolate x

Add 8 to both sides.

+ 8 + 8

Example 2: Undoing Addition

Intermediate

Solve .

Isolate y

Subtract 14 from both sides.

- 14 - 14

Example 3: Variable on Right

Advanced

Solve and graph.

Add 2

Rewrite

It is safer to read from the variable.

Common Pitfalls

Flipping Too Early

Students often flip the symbol when they subtract. (Correct). (WRONG). Subtraction never flips the symbol.

Real-Life Applications

Budgeting: You have $50 (maximum). You spent $20 on lunch. How much can you spend on dinner? . Solving gives . You can spend anything at or below $30.