Year 9: Solve symbolic linear equations

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

What is a Symbolic Linear Equation?

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