Lesson: Solving Inequalities

Introduction

In this lesson, we will learn how to solve inequalities, which are mathematical statements that compare expressions. An inequality shows that one expression is less than, greater than, less than or equal to, or greater than or equal to another expression.

Key Concepts

• Inequality Symbols:

  • Less than: $<$
  • Greater than: $>$
  • Less than or equal to: $\leq$
  • Greater than or equal to: $\geq$

• Solution of an Inequality: The set of values that make the inequality true.

Steps to Solve Inequalities

1. Isolate the variable on one side of the inequality.
2. Use inverse operations (addition, subtraction, multiplication, division) to solve for the variable.
3. Flip the inequality sign when multiplying or dividing by a negative number.

Example

Solve the inequality:
$3x + 5 < 14$

Step 1: Subtract 5 from both sides

$3x < 14 - 5$
$3x < 9$

Step 2: Divide both sides by 3

$x < \frac{9}{3}$
$x < 3$

Solution

The solution to the inequality is:
$x < 3$

Key Questions

• What is the difference between an equation and an inequality?
• How do you know when to flip the inequality sign?
• Can an inequality have more than one solution? If so, how do you represent that?

Conclusion

Solving inequalities requires similar techniques to solving equations, but with the added rule of flipping the inequality sign when dealing with negative numbers. Practice with different inequalities to become more comfortable with the process.