2.8.1
Solve Linear Equations
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Solving a Linear Equation
When we rearrange an equation, if we do something to one side, we must do the same to the other side of the equation. To solve the linear equation 6x - 3 = 5 + 2x to find x:
Check your answer
- So x = 2 does solve the equation.
1Number
1.1Using Numbers
1.1.1Equal Symbols1.1.2Negative Numbers1.1.3BIDMAS1.1.4Inverse Operations1.1.5End of Topic Test- Ordering1.1.6Factors1.1.7Multiples1.1.8Highest Common Factor1.1.9Lowest Common Multiple1.1.10Number of Ways to Do a Task1.1.11Number of Combinations1.1.12Number of Ways To Arrange Objects1.1.13End of Topic Test - Factors, Multiples & Combos1.1.14Standard Form1.1.15Ordinary Numbers to Standard Form1.1.16Addition in Standard Form1.1.17Subtraction in Standard Form1.1.18Multiplication in Standard Form1.1.19Division in Standard Form1.1.20Exam-Style Questions - Standard Form & Primes1.1.21Long Division1.1.22Prime Numbers1.1.23End of Topic Test - Standard Form & Long Division1.1.24Diagnostic Misconceptions - 1 NOT a Prime Number1.1.25Diagnostic Misconceptions - BIDMAS1.1.26Diagnostic Misconceptions - Adding Negatives
1.2Fractions, Decimals & Percentages
1.2.1Adding Fractions1.2.2Subtracting Fractions1.2.3Multiplying Fractions1.2.4Dividing Fractions1.2.5Mixed Fractions1.2.6Calculating Percentages of Numbers1.2.7Calculating Fractions of Numbers1.2.8Multiply Decimals1.2.9Place Value1.2.10Recurring Decimals1.2.11Exam-Style Questions - Recurring Decimals1.2.12Convert Fractions & Terminating Decimals1.2.13Convert Recurring Decimals1.2.14Convert Decimals & Percentages1.2.15Compare Decimals1.2.16Compare Fractions1.2.17Exam-Style Questions - Percentages1.2.18End of Topic Test - Fractions & Decimals1.2.19Diagnostic Misconceptions - Adding Fractions
1.3Powers & Roots
1.3.1Powers1.3.2Roots1.3.3Indices Advanced1.3.4Estimating Powers1.3.5Estimating Roots1.3.6Multiplying Powers1.3.7Dividing Powers1.3.8Power Raised to Power1.3.9Fractions Raised to a Power1.3.10Numbers Raised to Negative Powers1.3.11Roots of Numbers1.3.12Numbers to the Power of 1 & 01.3.13Surds1.3.14Simplify Surds1.3.15Rationalise Denominator1.3.16Exam-Style Questions - Indices1.3.17End of Topic Test - Powers & Roots1.3.18Diagnostic Misconceptions - Squaring1.3.19Diagnostic Misconceptions - Simplifying Surds
2Algebra
2.1Introduction to Algebra
2.1.1Algebra Basics2.1.2Substituting Values2.1.3Algebraic Vocabulary2.1.4Collecting Terms2.1.5End of Topic Test - Algebra Basics & Power Rules2.1.6Expanding Brackets I2.1.7Common Factors2.1.8Expanding Brackets II2.1.9Rearrange For x2.1.10Rearrange with Powers2.1.11Exam-Style Questions - Basics of Algebra2.1.12End of Topic Test - Expanding & Rearranging
2.2Manipulating Algebra
2.2.1How to Factorise2.2.2Factorising Quadratics2.2.3Algebraic Fractions - Addition & Subtraction2.2.4Algebraic Fractions - Multiplication & Division2.2.5Diagnostic Misconceptions - Common Denominators2.2.6Factorising Quadratics (tt)2.2.7Simplify algebraic fractions - cancelling factors2.2.8Simplify algebraic fractions - factorisation
2.3Proofs & Functions
2.4Straight Line Graphs
2.5Common Graphs
2.6Transformations & Tangents
2.7Properties of Graphs
2.8Solving Equations
2.8.1Solve Linear Equations2.8.2Linear Equations with Fractions2.8.3Solve Linear Equations Graphically2.8.4Quadratic ±2.8.5Factorise Quadratics2.8.6Quadratic Formula2.8.7Complete the Square2.8.8Solve Quadratics Graphically2.8.9End of Topic Test - Solving Equations2.8.10Simultaneous Equations2.8.11Quadratic Simultaneous Equations2.8.12Simultaneous Equations - Graphs2.8.13Simultaneous Equations - Word Problems2.8.14Approximate Solutions - Number of Iterations2.8.15Approximate Solutions - Iterations to 1 DP2.8.16Approximate Solutions - Iteration Formula2.8.17Exam-Style Questions - Simultaneous Equations2.8.18End of Topic Test - Simultaneous Equations2.8.19Diagnostic Misconceptions - Solving Quadratics
2.9Inequalities
2.10Sequences
2.10.1Nth Term Rules2.10.2Recurrence Relationships2.10.3Find Nth Term in Linear Sequence2.10.4Check If a Number is In a Sequence2.10.5Exam-Style Questions - Sequences2.10.6Arithmetic & Geometric Progressions2.10.7Key Sequences2.10.8Quadratic Sequences2.10.9Find Nth Term in Quadratic Sequence2.10.10Exam-Style Questions - Geometric Series2.10.11End of Topic Test - Sequences2.10.12Nth Term Rules (tt)
3Ratio
3.1Ratios in Practice
3.2Manipulating Ratios
3.2.1Simplifying Ratios3.2.2Turn Ratios into Equations3.2.3Ratio Notation & Reduction3.2.4End of Topic Test - Units & Ratios3.2.5Part : Part Ratio3.2.6Part : Whole Ratio3.2.7Two Ratios3.2.8Differences in Ratios3.2.9Fractions in Ratios3.2.10Numbers as Fractions3.2.11Ratios to Fractions3.2.12Exam-Style Questions - Ratios3.2.13End of Topic Test - Fractions & Ratios3.2.14Diagnostic Misconceptions - Combining Ratios
3.3Percentage & Interest
3.3.1Convert Percentages to Decimals3.3.2Convert Percentages to Fractions3.3.3Find the Percentage3.3.4More/Less Percentage3.3.5Price from Percentage Change3.3.6Calculate Percentage Change from Price3.3.7End of Topic Test - Percentages3.3.8Profit & Interest & Discount3.3.9Original Price after Discounts3.3.10Simple Interest3.3.11Compound Growth & Decay3.3.12Compound Interest3.3.13Compound Interest - After How Many Days?3.3.14End of Topic Test - Percentages in Finance
3.4Proportion
4Geometry
4.1Introduction to Geometry
4.1.1Geometry Basics4.1.2Geometry Basics 24.1.3Regular Polygons4.1.4Triangles & Angles4.1.5Midpoint4.1.6Bisectors & Perpendiculars4.1.7Locus4.1.8Angle rules4.1.9Parallel Angle Rules4.1.10Angles in a Polygon4.1.11Angles in a Triangle4.1.12Exam-Style Questions - Angles in Shapes4.1.13End of Topic Test - Geometry
4.2Triangles & Quadrilaterals
4.3Transformations
4.4Circle Basics
4.5Circle Theorems
4.5.1Perpendicular Bisector of a Chord4.5.2Angle at the Centre4.5.3Angle of a Semicircle4.5.4Opposite Angles in Cyclic Quadrilaterals4.5.5Tangent Lengths4.5.6Angle in the Same Segment4.5.7Alternate Segment Theorem4.5.8Exam-Style Questions - Circle Theorems4.5.9Diagnostic Misconceptions - Circumference & Radius
4.6Measurements & Units
4.7Calculating Area
4.8Triangle Formulae
4.93D Shapes
4.9.1Types of 3D Shape4.9.2Plans & Elevations4.9.3Nets4.9.4Volume of 3D Shapes4.9.5Volume of a Cuboid4.9.6Volume of a Cylinder4.9.7Volume of a Sphere4.9.8Volume of a Hemisphere4.9.9Volume of a Cone4.9.10Volume of a Pyramid4.9.11Surface Area & Composite Shapes4.9.12Surface Area of a Cuboid4.9.13Surface Area of a Cylinder4.9.14Surface Area of a Sphere/Hemisphere4.9.15Surface Area of a Cone4.9.16Exam-Style Questions - Volume
5Probability
5.1Introduction to Probability
5.2Representing Probabilities
5.3Probability Calculations
5.3.1Theoretical Probabilities5.3.2Multiple Events5.3.3Probability Calculations5.3.4Dependent Events5.3.5Independent Events5.3.6Probability Tree Diagram5.3.7Complex Tree Diagrams5.3.8Conditional Probability5.3.9Conditional Probability From a Two Way Table5.3.10Conditional Probability Venn Diagrams5.3.11Conditional Probability Tree Diagrams5.3.12Exam-Style Questions - Probability5.3.13End of Topic Test - Probability5.3.14Diagnostic Misconceptions - Denominator
6Statistics
6.1Introduction to Statistics
6.2Charts & Diagrams
6.2.1Bar Charts6.2.2Pie Charts6.2.3Stem & Leaf Diagrams6.2.4Back to Back Stem & Leaf Diagrams6.2.5End of Topic Test - Statistics6.2.6Pictograms6.2.7Time Series Graphs6.2.8Histograms6.2.9Histograms 26.2.10Frequency Polygons6.2.11Cumulative Frequency6.2.12Cumulative Frequency 26.2.13Scatter Graphs6.2.14Scatter Graphs - Predictions6.2.15Correlation & Causation6.2.16Exam-Style Questions - Cumulative Frequency
6.3Comparing Datasets
Jump to other topics
1Number
1.1Using Numbers
1.1.1Equal Symbols1.1.2Negative Numbers1.1.3BIDMAS1.1.4Inverse Operations1.1.5End of Topic Test- Ordering1.1.6Factors1.1.7Multiples1.1.8Highest Common Factor1.1.9Lowest Common Multiple1.1.10Number of Ways to Do a Task1.1.11Number of Combinations1.1.12Number of Ways To Arrange Objects1.1.13End of Topic Test - Factors, Multiples & Combos1.1.14Standard Form1.1.15Ordinary Numbers to Standard Form1.1.16Addition in Standard Form1.1.17Subtraction in Standard Form1.1.18Multiplication in Standard Form1.1.19Division in Standard Form1.1.20Exam-Style Questions - Standard Form & Primes1.1.21Long Division1.1.22Prime Numbers1.1.23End of Topic Test - Standard Form & Long Division1.1.24Diagnostic Misconceptions - 1 NOT a Prime Number1.1.25Diagnostic Misconceptions - BIDMAS1.1.26Diagnostic Misconceptions - Adding Negatives
1.2Fractions, Decimals & Percentages
1.2.1Adding Fractions1.2.2Subtracting Fractions1.2.3Multiplying Fractions1.2.4Dividing Fractions1.2.5Mixed Fractions1.2.6Calculating Percentages of Numbers1.2.7Calculating Fractions of Numbers1.2.8Multiply Decimals1.2.9Place Value1.2.10Recurring Decimals1.2.11Exam-Style Questions - Recurring Decimals1.2.12Convert Fractions & Terminating Decimals1.2.13Convert Recurring Decimals1.2.14Convert Decimals & Percentages1.2.15Compare Decimals1.2.16Compare Fractions1.2.17Exam-Style Questions - Percentages1.2.18End of Topic Test - Fractions & Decimals1.2.19Diagnostic Misconceptions - Adding Fractions
1.3Powers & Roots
1.3.1Powers1.3.2Roots1.3.3Indices Advanced1.3.4Estimating Powers1.3.5Estimating Roots1.3.6Multiplying Powers1.3.7Dividing Powers1.3.8Power Raised to Power1.3.9Fractions Raised to a Power1.3.10Numbers Raised to Negative Powers1.3.11Roots of Numbers1.3.12Numbers to the Power of 1 & 01.3.13Surds1.3.14Simplify Surds1.3.15Rationalise Denominator1.3.16Exam-Style Questions - Indices1.3.17End of Topic Test - Powers & Roots1.3.18Diagnostic Misconceptions - Squaring1.3.19Diagnostic Misconceptions - Simplifying Surds
2Algebra
2.1Introduction to Algebra
2.1.1Algebra Basics2.1.2Substituting Values2.1.3Algebraic Vocabulary2.1.4Collecting Terms2.1.5End of Topic Test - Algebra Basics & Power Rules2.1.6Expanding Brackets I2.1.7Common Factors2.1.8Expanding Brackets II2.1.9Rearrange For x2.1.10Rearrange with Powers2.1.11Exam-Style Questions - Basics of Algebra2.1.12End of Topic Test - Expanding & Rearranging
2.2Manipulating Algebra
2.2.1How to Factorise2.2.2Factorising Quadratics2.2.3Algebraic Fractions - Addition & Subtraction2.2.4Algebraic Fractions - Multiplication & Division2.2.5Diagnostic Misconceptions - Common Denominators2.2.6Factorising Quadratics (tt)2.2.7Simplify algebraic fractions - cancelling factors2.2.8Simplify algebraic fractions - factorisation
2.3Proofs & Functions
2.4Straight Line Graphs
2.5Common Graphs
2.6Transformations & Tangents
2.7Properties of Graphs
2.8Solving Equations
2.8.1Solve Linear Equations2.8.2Linear Equations with Fractions2.8.3Solve Linear Equations Graphically2.8.4Quadratic ±2.8.5Factorise Quadratics2.8.6Quadratic Formula2.8.7Complete the Square2.8.8Solve Quadratics Graphically2.8.9End of Topic Test - Solving Equations2.8.10Simultaneous Equations2.8.11Quadratic Simultaneous Equations2.8.12Simultaneous Equations - Graphs2.8.13Simultaneous Equations - Word Problems2.8.14Approximate Solutions - Number of Iterations2.8.15Approximate Solutions - Iterations to 1 DP2.8.16Approximate Solutions - Iteration Formula2.8.17Exam-Style Questions - Simultaneous Equations2.8.18End of Topic Test - Simultaneous Equations2.8.19Diagnostic Misconceptions - Solving Quadratics
2.9Inequalities
2.10Sequences
2.10.1Nth Term Rules2.10.2Recurrence Relationships2.10.3Find Nth Term in Linear Sequence2.10.4Check If a Number is In a Sequence2.10.5Exam-Style Questions - Sequences2.10.6Arithmetic & Geometric Progressions2.10.7Key Sequences2.10.8Quadratic Sequences2.10.9Find Nth Term in Quadratic Sequence2.10.10Exam-Style Questions - Geometric Series2.10.11End of Topic Test - Sequences2.10.12Nth Term Rules (tt)
3Ratio
3.1Ratios in Practice
3.2Manipulating Ratios
3.2.1Simplifying Ratios3.2.2Turn Ratios into Equations3.2.3Ratio Notation & Reduction3.2.4End of Topic Test - Units & Ratios3.2.5Part : Part Ratio3.2.6Part : Whole Ratio3.2.7Two Ratios3.2.8Differences in Ratios3.2.9Fractions in Ratios3.2.10Numbers as Fractions3.2.11Ratios to Fractions3.2.12Exam-Style Questions - Ratios3.2.13End of Topic Test - Fractions & Ratios3.2.14Diagnostic Misconceptions - Combining Ratios
3.3Percentage & Interest
3.3.1Convert Percentages to Decimals3.3.2Convert Percentages to Fractions3.3.3Find the Percentage3.3.4More/Less Percentage3.3.5Price from Percentage Change3.3.6Calculate Percentage Change from Price3.3.7End of Topic Test - Percentages3.3.8Profit & Interest & Discount3.3.9Original Price after Discounts3.3.10Simple Interest3.3.11Compound Growth & Decay3.3.12Compound Interest3.3.13Compound Interest - After How Many Days?3.3.14End of Topic Test - Percentages in Finance
3.4Proportion
4Geometry
4.1Introduction to Geometry
4.1.1Geometry Basics4.1.2Geometry Basics 24.1.3Regular Polygons4.1.4Triangles & Angles4.1.5Midpoint4.1.6Bisectors & Perpendiculars4.1.7Locus4.1.8Angle rules4.1.9Parallel Angle Rules4.1.10Angles in a Polygon4.1.11Angles in a Triangle4.1.12Exam-Style Questions - Angles in Shapes4.1.13End of Topic Test - Geometry
4.2Triangles & Quadrilaterals
4.3Transformations
4.4Circle Basics
4.5Circle Theorems
4.5.1Perpendicular Bisector of a Chord4.5.2Angle at the Centre4.5.3Angle of a Semicircle4.5.4Opposite Angles in Cyclic Quadrilaterals4.5.5Tangent Lengths4.5.6Angle in the Same Segment4.5.7Alternate Segment Theorem4.5.8Exam-Style Questions - Circle Theorems4.5.9Diagnostic Misconceptions - Circumference & Radius
4.6Measurements & Units
4.7Calculating Area
4.8Triangle Formulae
4.93D Shapes
4.9.1Types of 3D Shape4.9.2Plans & Elevations4.9.3Nets4.9.4Volume of 3D Shapes4.9.5Volume of a Cuboid4.9.6Volume of a Cylinder4.9.7Volume of a Sphere4.9.8Volume of a Hemisphere4.9.9Volume of a Cone4.9.10Volume of a Pyramid4.9.11Surface Area & Composite Shapes4.9.12Surface Area of a Cuboid4.9.13Surface Area of a Cylinder4.9.14Surface Area of a Sphere/Hemisphere4.9.15Surface Area of a Cone4.9.16Exam-Style Questions - Volume
5Probability
5.1Introduction to Probability
5.2Representing Probabilities
5.3Probability Calculations
5.3.1Theoretical Probabilities5.3.2Multiple Events5.3.3Probability Calculations5.3.4Dependent Events5.3.5Independent Events5.3.6Probability Tree Diagram5.3.7Complex Tree Diagrams5.3.8Conditional Probability5.3.9Conditional Probability From a Two Way Table5.3.10Conditional Probability Venn Diagrams5.3.11Conditional Probability Tree Diagrams5.3.12Exam-Style Questions - Probability5.3.13End of Topic Test - Probability5.3.14Diagnostic Misconceptions - Denominator
6Statistics
6.1Introduction to Statistics
6.2Charts & Diagrams
6.2.1Bar Charts6.2.2Pie Charts6.2.3Stem & Leaf Diagrams6.2.4Back to Back Stem & Leaf Diagrams6.2.5End of Topic Test - Statistics6.2.6Pictograms6.2.7Time Series Graphs6.2.8Histograms6.2.9Histograms 26.2.10Frequency Polygons6.2.11Cumulative Frequency6.2.12Cumulative Frequency 26.2.13Scatter Graphs6.2.14Scatter Graphs - Predictions6.2.15Correlation & Causation6.2.16Exam-Style Questions - Cumulative Frequency
6.3Comparing Datasets
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