Year 8 - Maths
Rearranging to solve 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 recognise that equations with unknowns on both sides of the equation can be manipulated so that the unknowns are on one side and then solve this equation.
Key Notes
- Any linear equation written in the form Ax + B = C can be solved.
- Like terms can be collected onto one side of an equation in order to write it in the form Ax + B = C.
- An equation that had unknowns on both sides can then be solved.
Vocabulary To Learn
- Equation: An equation is used to show two expressions that are equal to each other.
Common Mistakes To Avoid
- To subtract from both the variable and numerical terms when subtracting from both sides.
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. Like terms can be collected onto one side of an equation in order to write it in 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: To subtract from both the variable and numerical terms when subtracting from both sides. Correction: To subtract $$2$$ from $$5x+3$$ leaves $$5x+1$$, not $$3x+1$$. Use visual representations like balance scales and bar models to show this.
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
- Securing understanding of equality Study Guide
- Solution to an equation Study Guide
- Solving complex linear equations 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.