Year 8 - Maths
Solving complex linear equations
Solving linear equations
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will learn how to find a value that satisfies a linear relationship when one value is known both with a single step operation, and multiple step operations. A variety of cases are explored including using brackets and rearranging.
Lesson Summary
You will learn to solve complex linear equations, including those involving reciprocals.
Key Notes
- Any linear equation written in the form Ax + B = C can be solved.
- Equations involving division by a constant can be manipulated to reach the form Ax + B = C.
- Equations involving division by a variable can be manipulated to reach the form Ax + B = C.
Vocabulary To Learn
- Equation: An equation is used to show two expressions that are equal to each other.
Common Mistakes To Avoid
- Pupils often "multiply through by $$5$$" and turn $${{2x+1}\over5}={10}$$ into $${{10x+5}}={50}$$
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Any linear equation written in the form Ax + B = C can be solved. Equations involving division by a constant can be manipulated to reach the form Ax + B = C.
2. Use this key word in a maths sentence and explain it clearly. 'Equation'
An equation is used to show two expressions that are equal to each other. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils often "multiply through by $$5$$" and turn $${{2x+1}\over5}={10}$$ into $${{10x+5}}={50}$$. Correction: Use equivalent fractions as opposed to multiplying through. In one simple step $${{2x+1}\over5}={10}$$ becomes $${{2x+1}\over5}={50\over5}$$.
More Lessons In This Unit
- Brackets in equations Study Guide
- Checking understanding of algebraic notation Study Guide
- Different types of equations Study Guide
- Equality in an equation Study Guide
- Many equations, one solution Study Guide
- Preparing to solve two step linear equations Study Guide
- Problem solving with linear equations Study Guide
- Rearranging to solve linear equations Study Guide
- Securing understanding of equality Study Guide
- Solution to an equation Study Guide
- Solving complex linear equations involving brackets Study Guide
- Solving linear equations graphically using technology Study Guide
- Solving linear equations where brackets are used Study Guide
- Solving simple linear equations with a multiplicative step Study Guide
- Solving simple linear equations with an additive step Study Guide
- Solving two step linear equations Study Guide
Browse all guides in the Year 8 Maths guide library.