Undo the outside operation first
To solve x + 5 = 17, remove 5 from both sides before doing anything else.
Use the inverse of plus 5, which is subtract 5.
Year 8
Solve two-step linear equations
Solve two-step linear equations accurately, use inverse operations in the correct order, and explain why balanced equations stay equal.
Lesson overview
Algebra - equations and inverse operations
An equation is like a balance. Both sides have the same value, so whatever we do to one side must also be done to the other. In a two-step equation, start by undoing the addition or subtraction, then undo the multiplication or division. Working in reverse order keeps the structure clear and helps isolate the unknown.
Reverse the order of operations
In 3x + 4 = 19, subtract 4 first, then divide by 3.
| Equation | Step 1 | Step 2 |
|---|---|---|
| 3x + 4 = 19 | 3x = 15 | x = 5 |
Do not divide first. The 4 is added after the multiplication.
Keep both sides balanced
If 2y - 3 = 11, add 3 to both sides and then divide by 2.
add 3 to both sides
divide both sides by 2
Each step must happen on both sides, not just beside the letter.
Worked example
Solve 4x + 7 = 23.
| Start | Subtract 7 | Divide by 4 |
|---|---|---|
| 4x + 7 = 23 | 4x = 16 | x = 4 |
- Start with 4x + 7 = 23.
- Subtract 7 from both sides to get 4x = 16.
- Divide both sides by 4 to get x = 4.
- Check by substituting: 4(4) + 7 = 23, so the solution is correct.
Try it
Look at the order of operations in the equation, then undo them in reverse while keeping both sides balanced.
Question 1
Solve x + 6 = 14.
Question 2
Solve 3x + 5 = 20.
| Subtract 5 | Then divide by 3 |
|---|---|
| 3x = 15 | x = 5 |
Question 3
Solve 2y - 4 = 10.
Question 4
Which is the correct first step for 5a + 9 = 29?
Question 5
A cinema ticket costs 3 pounds plus a booking fee of 2 pounds. The total is 17 pounds. How many tickets were bought?
Common mistakes
Watch for these when working through the lesson.
- Undoing the multiplication before undoing the addition or subtraction.
- Changing only one side of the equation.
- Stopping after the first step instead of fully isolating the variable.
Related topics
These ideas fit closely with this lesson.
- Expand single brackets.
- Plot and interpret linear graphs from y = mx + c.
- Substitute into formulae.