Solve equations: complete the solution

key notes :

Understanding the Equation

• An equation is a statement that two expressions are equal.
• It often contains a variable (e.g., x) that you need to solve for.

Goal of Solving an Equation

• Find the value of the variable that makes the equation true.

Types of Equations

• One-step equations (e.g., x + 5 = 9)
• Two-step equations (e.g., 2x – 3 = 7)
• Multi-step equations (e.g., 3x + 2 = 2x + 7)
• Equations with variables on both sides
• Equations with brackets or fractions

Basic Steps to Solve Equations

• Simplify both sides (remove brackets, combine like terms).
• Move variable terms to one side and constant terms to the other.
• Isolate the variable using inverse operations (add, subtract, multiply, divide).
• Solve for the variable.
• Check your solution by substituting back into the original equation.

Inverse Operations

Used to “undo” operations:

Addition ↔ Subtraction

Multiplication ↔ Division

Keeping the Equation Balanced

• Whatever you do to one side, you must do to the other side.

Common Mistakes to Avoid

• Forgetting to apply operations to both sides
• Sign errors (positive/negative)
• Not simplifying expressions fully
• Not checking your final answer

Special Cases

• No solution: Both sides can’t be equal (e.g., x + 2 = x + 5)
• Infinite solutions: Both sides are exactly the same (e.g., 2x + 1 = 2x + 1)

Learn with an example

Let’s practice!