🔮 Algebra Realm · Equations

Brackets on both sides

Brackets on both sides focuses on how to expand and simplify both sides before collecting variable terms. In this lesson, focus on algebraic expressions preserve structure.

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Understand Brackets on both sides

Brackets on both sides focuses on how to expand and simplify both sides before collecting variable terms. In this lesson, focus on algebraic expressions preserve structure.

Algebraic expressions preserve structure. Terms can combine only when their variable parts match, and expanding a bracket means multiplying every term inside it. For brackets on both sides, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Brackets on both sides: Algebraic expressions preserve structure. Substitute a small value such as x = 2 into both versions and compare the totals. Keep the brackets on both sides representation visible until the final line.

Picture the idea

Use colour-coded tiles to group matching variable terms and distribute factors across brackets. Use the model to explain one change you notice while working on brackets on both sides.

Check as you go

Substitute a small value such as x = 2 into both versions and compare the totals. Write that check beside the final brackets on both sides answer.

Key vocabulary

termcoefficientconstantlike termsexpandbracketsboth

Rules and key facts

2(x + 5) = 3(x + 1) gives 2x + 10 = 3x + 3, so x = 7.

  • Identify terms, coefficients and constants.
  • Group only like terms or distribute the bracket multiplier.
  • Write the simplified expression in a clear order.
  • Substitute a test value to compare the original and simplified forms. Record the check explicitly for brackets on both sides.

Step-by-step method

  1. Identify terms, coefficients and constants.
  2. Group only like terms or distribute the bracket multiplier.
  3. Write the simplified expression in a clear order.
  4. Substitute a test value to compare the original and simplified forms. Record the check explicitly for brackets on both sides.

What you need first

  • Recognise the vocabulary: term, coefficient, constant.
  • Be able to explain the purpose of brackets on both sides before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Formula writing
  • Spreadsheet rules

Visual / interactive

See the idea, then move it around

Skip to Practice

Use colour-coded tiles to group matching variable terms and distribute factors across brackets. Use the model to explain one change you notice while working on brackets on both sides.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
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Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Brackets on both sides — Solve 5x + 2 = 3x + 6. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 2 = 6. Subtract 2, then divide by 2: x = 2. Final answer: 2. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Identify terms, coefficients and constants.
  2. Group only like terms or distribute the bracket multiplier.
  3. Write the simplified expression in a clear order.
Secure example

Use the normal method

Given information: Brackets on both sides — Solve 5x + 14 = 3x + 34. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 14 = 34. Subtract 14, then divide by 2: x = 10. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Solve and check against both original brackets.

Challenge example

Stretch the idea

Given information: Brackets on both sides — Solve 5x + 13 = 3x + 27. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 13 = 27. Subtract 13, then divide by 2: x = 7. Final answer: 7. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Brackets on both sides — Solve 5x + 12 = 3x + 20. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 12 = 20. Subtract 12, then divide by 2: x = 4. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Use a separate expansion line for each side.

Common mistakes

  • Combining unlike terms. This is a key trap when answering brackets on both sides questions.
  • Multiplying only the first term inside a bracket.

How to check your answer

Substitute a small value such as x = 2 into both versions and compare the totals. Write that check beside the final brackets on both sides answer.

Extension challenge

Create a brackets on both sides problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Brackets on both sides challenge

Use tile forge controls to solve three checked brackets on both sides rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Study cards

Core idea

Brackets on both sides: Algebraic expressions preserve structure. Substitute a small value such as x = 2 into both versions and compare the totals. Keep the brackets on both sides representation visible until the final line.

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Key vocabulary

term · coefficient · constant · like terms · expand · brackets · both

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Rules

Identify terms, coefficients and constants. Group only like terms or distribute the bracket multiplier. Write the simplified expression in a clear order. Substitute a test value to compare the original and simplified forms. Record the check explicitly for brackets on both sides.

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Formula / fact

2(x + 5) = 3(x + 1) gives 2x + 10 = 3x + 3, so x = 7.

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Foundation example

Given information: Brackets on both sides — Solve 5x + 2 = 3x + 6. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 2 = 6. Subtract 2, then divide by 2: x = 2. Final answer: 2. Check: substitute or compare with the original information to confirm the result fits the question.

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Secure example

Given information: Brackets on both sides — Solve 5x + 14 = 3x + 34. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 14 = 34. Subtract 14, then divide by 2: x = 10. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Brackets on both sides — Solve 5x + 13 = 3x + 27. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 13 = 27. Subtract 13, then divide by 2: x = 7. Final answer: 7. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Brackets on both sides — Solve 5x + 12 = 3x + 20. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 12 = 20. Subtract 12, then divide by 2: x = 4. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Combining unlike terms. This is a key trap when answering brackets on both sides questions.

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Exam tip

For brackets on both sides, show the key representation before the final calculation. Use this final check: Substitute a small value such as x = 2 into both versions and compare the totals.

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Real-world use

Formula writing, Spreadsheet rules

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Checklist

I can explain brackets on both sides, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Brackets on both sides

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Simple explanation

Brackets on both sides: Algebraic expressions preserve structure. Substitute a small value such as x = 2 into both versions and compare the totals. Keep the brackets on both sides representation visible until the final line.

Think of brackets on both sides as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Identify terms, coefficients and constants.
  2. Group only like terms or distribute the bracket multiplier.
  3. Write the simplified expression in a clear order.
  4. Substitute a test value to compare the original and simplified forms. Record the check explicitly for brackets on both sides.

Hint 1

Start by naming the given information and the exact result required for brackets on both sides.

Hint 2

Identify terms, coefficients and constants.

Full worked solution

Given information: Brackets on both sides — Solve 5x + 2 = 3x + 6. Method choice: use the brackets on both sides method and show each step with the stated values. Calculation or reasoning: Subtract 3x: 2x + 2 = 6. Subtract 2, then divide by 2: x = 2. Final answer: 2. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Identify terms, coefficients and constants. → Group only like terms or distribute the bracket multiplier. → Write the simplified expression in a clear order. → Substitute a test value to compare the original and simplified forms. Record the check explicitly for brackets on both sides.

Common mistake warning

Combining unlike terms. This is a key trap when answering brackets on both sides questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain brackets on both sides in my own words.
  • I can use these words accurately: term, coefficient, constant.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Combining unlike terms.
  • I can apply this check: Substitute a small value such as x = 2 into both versions and compare the totals.
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