What is an Equation?

An equation is a mathematical statement that two expressions are equal.

Parts of an Equation

$3x + 5 = 14$

• Left side: $3x + 5$
• Equals sign: $=$
• Right side: $14$

What is a Solution?

A solution is a value that makes the equation true.

For $3x + 5 = 14$:

• Is $x = 2$ a solution? $3(2) + 5 = 6 + 5 = 11 \neq 14$ ❌
• Is $x = 3$ a solution? $3(3) + 5 = 9 + 5 = 14$ ✓

So $x = 3$ is the solution!

The Balance Principle

Think of an equation like a balance scale. Both sides must stay equal.

$\text{Left side} = \text{Right side}$

Key Rule: Whatever you do to one side, you must do to the other side to keep it balanced.

Our Goal

When solving equations, we want to isolate the variable (get it alone on one side).

$? \rightarrow x = \text{number}$

In the next lessons, we'll learn techniques to isolate the variable step by step.