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: $2\left(5\right)=10$ ✓

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