Year 7: Solve linear equations

Solving linear equations means finding the value of the unknown variable (usually 'x') that makes the equation true. Here's how to do it:

Key Principles

• Isolate the Variable: Your goal is to get the variable by itself on one side of the equals sign.
• Use Inverse Operations: To get rid of a number, you use its inverse operation (addition and subtraction, multiplication and division).
• Do the Same to Both Sides: Whatever you do to one side of the equation, you MUST do to the other side to keep it balanced.

Steps to Solve a Linear Equation

1. Simplify: Remove any brackets or combine like terms if possible.
2. Add or Subtract: Add or subtract the same number to both sides of the equation.
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 see if it makes the equation true.

Examples

Example 1: 2x + 3 = 7

Subtract 3 from both sides: 2x = 4

Divide both sides by 2: x = 2

Example 2:x/3 - 1 = 2

Add 1 to both sides: x/3 = 3

Multiply both sides by 3: x = 9