8 · Variables on Both Sides
Solve equations with the variable on both sides, including brackets and negatives.
What your child learns
- Move all x terms to one side
- Move all numbers to the other side
- Expand brackets first when you see them
Example
4(x − 3) + 2 = 2x + 12 → 4x − 10 = 2x + 12 → 2x = 22 → x = 11.
Mini lesson: Variables on Both Sides
Goal: Solve equations where x appears on both sides.
Tip: subtract the smaller x term from both sides to avoid negatives.
Worked example
Solve 4(x − 3) + 2 = 2x + 12.
- Expand: 4x − 12 + 2 = 2x + 12
- Simplify: 4x − 10 = 2x + 12
- Subtract 2x: 2x − 10 = 12
- Add 10: 2x = 22
- Divide by 2: x = 11. Check: 4(8) + 2 = 34 and 22 + 12 = 34 ✔
Common mistakes
- Forgetting to multiply the −3 by 4 when expanding.
- Moving a term without changing its sign.
Practice questions
A taste of the questions in BloomTracks – the app makes fresh ones every time and adjusts the level as your child answers.
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Question 1 · Level 1
To solve 5x + 4 = 3x + 20, what is a good first step?
- Subtract 5x from one side
- Divide both sides by 5
- Subtract 3x from both sides
- Add 3x to both sides
Show the answer
Answer: Subtract 3x from both sides
Subtract 3x from both sides: 2x + 4 = 20. Then solve: x = 8.
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Question 2 · Level 3
Solve: 9x − 1 = 5x + 7
Show the answer
Answer: 2
x = 2
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Question 3 · Level 5
Solve: 4(x − 3) + 2 = 2x + 12
Show the answer
Answer: 11
x = 11. Check: left = 34, right = 34. ✔
Try it at home
Compare two phone plans and find when they cost the same.
Key takeaway
Subtract the smaller x term to keep things positive.
Practise 8 · variables on both sides with Bloomie
Bloomie reads every question aloud, listens to spoken answers and adapts the difficulty one question at a time.