Algebra Lesson: Solving Two-Step Linear Equations, Summaries of Mathematics

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📘 Algebra Lesson: Solving Two-Step Linear

Equations

🎯 Learning Objectives

By the end of this lesson, you will be able to:

 Define what a two-step linear equation is.  Explain the reasoning behind solving linear equations step by step.  Apply inverse operations to isolate the variable.  Solve two-step equations involving both integers and fractions.  Check your solutions by substitution.

📖 Introduction to Two-Step Linear Equations

In Algebra, equations are statements that assert the equality of two expressions. A two-step linear equation is a type of algebraic equation that can be solved using two inverse operations. These equations typically contain one variable and require two steps to isolate that variable.

General form:

ax + b = c

Where:

 x is the variable you are solving for  a, b, and c are known numbers (constants)

These are called "two-step" because:

1. The constant b is added to or subtracted from the variable term.
2. The variable term ax is being multiplied or divided.

🛠 ️ Why Use Inverse Operations?

Inverse operations are pairs of operations that cancel each other out:

 Addition ⟷ Subtraction  Multiplication ⟷ Division

To isolate a variable, we reverse the operations that have been applied to it.

🠀 Step-by-Step Method

Let’s solve this example:

Example equation:

4x - 5 = 11

Step 1: Eliminate the constant Add 5 to both sides:

4x - 5 + 5 = 11 + 5

4x = 16

Step 2: Eliminate the coefficient Divide both sides by 4:

4x / 4 = 16 / 4

x = 4

✅ Check Your Solution

Substitute x=4 into the original equation:

4(4) - 5 = 16 - 5 = 11

✔ Correct!

✍ ️ More Examples

Example 1:

3x + 7 = 19

Subtract 7: 3x = 12

Divide by 3: x = 4

Example 2:

-2x + 6 = 0

To solve two-step equations, work backward using inverse operations. Always maintain balance by performing the same operation on both sides of the equation.