Linear Equations

What is a Linear Equation?

An equation where the variable has no exponents. Just $x$, not $x^2$ or $x^3$.

The simplest form: $ax + b = c$

What Does “Solving” Mean?

Finding the value of $x$ that makes the equation true.

If $2x + 3 = 7$, we want to find what $x$ equals.

The Key Idea

Think of an equation like a balance scale.

Whatever you do to one side, you must do to the other. This keeps it balanced.

Solving Step by Step

Goal: Get $x$ alone on one side.

Method: Undo operations by doing the opposite.

• Addition? Subtract.
• Subtraction? Add.
• Multiplication? Divide.
• Division? Multiply.

Example

The Pattern

1. Undo addition/subtraction — get the term with $x$ alone
2. Undo multiplication/division — get $x$ by itself
3. Check — plug your answer back in to verify