Year 9: Solve symbolic linear equations

This cheat sheet will guide you through solving simple algebraic equations.

A symbolic linear equation is an equation where the highest power of the variables is 1. It always involves a linear relationship – a straight line when graphed.

Key rules

• Isolate the variable: Your goal is to get the variable (usually 'x') by itself on one side of the equation.
• Inverse operations: To undo an operation, you use its inverse.
  • Addition becomes subtraction
  • Multiplication becomes division
• Do what you do to both sides: Whatever operation you perform on one side of the equation, you *must* do it to the other side to maintain equality. This is the most important rule!

Steps to solve

1. Simplify: Remove any brackets or combine like terms if possible.
2. Add or subtract: Add or subtract the same number from both sides.
3. Multiply or divide: Multiply or divide both sides by the same number.
4. Check your answer: Substitute your solution back into the original equation to ensure it is correct.

Example

Example: 2x + 5 = 11

1. Subtract 5 from both sides: 2x = 6

2. Divide both sides by 2: x = 3