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Linear Equations (AQA GCSE Maths)

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  • FrontSolving Linear Equations

    What is the greatest power of x in a linear equation?

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  • What is the greatest power of x in a linear equation?

    The greatest power of x in a linear equation is 1.

    There is no term in x2 or any higher power.

  • What does 'isolate the variable' mean?

    Isolate the variable means to get the variable term, e.g. x, by itself on one side of the equation.

  • What are inverse operations?

    Inverse operations are the opposite operations to what has already happened to the variable.

    E.g. In the expression 4 x, x is being multiplied by 4.
    The inverse operation is to divide by 4.

    Examples of inverse operations are:

    • Add and subtract

    • Multiply and divide

    • Square and take the square root

  • True or False?

    To solve a linear equation, e.g. 3 x plus 4 equals 13, you need to isolate the variable by carrying out inverse operations to both sides.

    True.

    To solve a linear equation, you need to isolate the variable, (get the letter on its own), by carrying out inverse operations to both sides.

    E.g.

    3 x plus 4 equals 13 table row cell negative 4 end cell cell space space space space space space space space space space space space space space space space space space space space minus 4 end cell end table 3 x equals 9 divided by 3 space space space space space space space space space space space space space space space space space space space space space divided by 3 x equals 3

  • What is the order of inverse operations to solve a linear equation of the form a x plus b equals c to find x.

    To solve a linear equation of the form a x plus b equals c:

    • First subtract b from both sides

    • Then divide both sides by a

  • True or False?

    If a linear equation contains the unknown variable on both sides, you should first collect the variable terms on one side.

    E.g. 8 x plus 7 equals 2 x plus 11.

    True.

    If a linear equation contains the unknown variable on both sides, you should first collect the variable terms on one side.

    E.g.

    table row cell 8 x plus 7 end cell equals cell 2 x plus 11 end cell row cell 6 x plus 7 end cell equals 11 end table

  • What is the first step to solve a linear equation with brackets?

    E.g. 4 open parentheses x plus 6 close parentheses equals 32.

    The first step to solve a linear equation with brackets is to expand the brackets (on both sides if necessary).

    E.g.

    table row cell 4 open parentheses x plus 6 close parentheses end cell equals 32 row cell 4 x plus 24 end cell equals 32 end table

  • What is the first step to solve a linear equation with fractions?

    E.g. fraction numerator x plus 9 over denominator 2 end fraction equals fraction numerator 3 x minus 1 over denominator 4 end fraction.

    The first step to solve a linear equation with fractions is to remove the fractions by multiplying both sides by the denominators.

    E.g.

    table row cell fraction numerator x plus 9 over denominator 2 end fraction end cell equals cell fraction numerator 3 x minus 1 over denominator 4 end fraction end cell row cell 4 open parentheses x plus 9 close parentheses end cell equals cell 2 open parentheses 3 x minus 1 close parentheses end cell row blank blank blank end table

  • After solving a linear equation, how can you check your answer to see if it is correct?

    After solving a linear equation, you should substitute your answer back into the equation to check if it is correct.

    This is a quick way to spot if you have made any mistakes.

Previous:Algebraic ProofNext:Quadratic Equations

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation