Year 7: Solve Linear Equations

Solving Linear Equations - Key Principles

• Isolate the Variable: Your goal is to get the variable by itself on one side of the equals sign
• Use Inverse Operations: Do the opposite operation to move terms (add/subtract, multiply/divide)
• Keep It Balanced: Whatever you do to one side, you MUST do to the other side

Steps to Solve Linear Equations

1. Simplify if needed: Expand brackets or combine like terms on each side
2. Move constants: Add or subtract to move numbers away from the variable term
3. Isolate the variable: Multiply or divide to get the variable by itself
4. Check your answer: Substitute your solution back into the original equation

Examples

Example 1: 2x + 3 = 7

1. Subtract 3 from both sides: 2x = 4
2. Divide both sides by 2: x = 2
3. Check: 2(2) + 3 = 4 + 3 = 7 ✓

Example 2: x/3 - 1 = 2

1. Add 1 to both sides: x/3 = 3
2. Multiply both sides by 3: x = 9
3. Check: 9/3 - 1 = 3 - 1 = 2 ✓

Example 3: 3(x - 2) = 12

1. Expand: 3x - 6 = 12
2. Add 6 to both sides: 3x = 18
3. Divide by 3: x = 6
4. Check: 3(6 - 2) = 3(4) = 12 ✓

Example 4: 5x - 2 = 3x + 8

1. Subtract 3x from both sides: 2x - 2 = 8
2. Add 2 to both sides: 2x = 10
3. Divide by 2: x = 5
4. Check: 5(5) - 2 = 25 - 2 = 23, and 3(5) + 8 = 15 + 8 = 23 ✓