Year 10: Solve linear equations

What is a Linear Equation?

A linear equation is an equation where the highest power of the variable (usually 'x') is 1. It represents a straight line when graphed. It always has one solution.

Steps to Solve Linear Equations

1. Isolate the Variable: Your goal is to get 'x' by itself on one side of the equation.
2. Use Inverse Operations: To undo addition, subtract; to undo multiplication, divide; to undo division, multiply; to undo multiplication, divide. Remember to do the *same* operation to *both* sides of the equation to keep it balanced.
3. Simplify: Combine like terms if needed.
4. Check your Solution: Substitute your solution back into the original equation to make sure it makes the equation true.

Example

Solve: 2x + 3 = 7

1. Subtract 3 from both sides: 2x = 4
2. Divide both sides by 2: x = 2
3. Check: 2(2) + 3 = 7 -> 4 + 3 = 7 -> 7 = 7 (Correct!)

Important Reminders

• Always keep the equation balanced – whatever you do to one side, do to the other.
• Don’t move constant terms (numbers without a variable) from one side to the other.