Year 7: Solve Simple Linear Equations

What is a Linear Equation?

A linear equation is an equation where the variable (usually x) has a power of 1. It can be written as: x + a = b or ax = b

Steps to Solve Simple Linear Equations

1. Identify the operation: Is the variable being added to, subtracted from, multiplied, or divided?
2. Do the opposite operation: To isolate x, undo what's happening to it
3. Do it to both sides: Keep the equation balanced by doing the same operation on both sides
4. Check your answer: Substitute your answer back into the original equation

Examples

Example 1: x + 3 = 7

1. The 3 is being added to x, so subtract 3 from both sides
2. x + 3 - 3 = 7 - 3
3. x = 4
4. Check: 4 + 3 = 7 ✓

Example 2: 2x = 10

1. The x is being multiplied by 2, so divide both sides by 2
2. 2x / 2 = 10 / 2
3. x = 5
4. Check: 2(5) = 10 ✓

Example 3: x - 5 = 2

1. The 5 is being subtracted from x, so add 5 to both sides
2. x - 5 + 5 = 2 + 5
3. x = 7
4. Check: 7 - 5 = 2 ✓

Inverse Operations

Remember these opposite operations:

• Addition <-> Subtraction
• Multiplication <-> Division