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**Solving Linear Equations**

Which level would you like to study? Level 5 Level 6 Level 7 Worksheet

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Level 5 Objective: Be able to solve linear equations with an unknown on one side.

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**4a = 24 a = 24 4 = 6 Low level 5 This means “4 multiplied by a”**

What is the inverse operation? = 6 Division

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**b = 3 5 b = 3 x 5 = 15 Low Level 5 This means “b divided by 5”**

What is the inverse operation? = 15 Multiplication

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**3a + 8 = 35 3a = 35 - 8 3a = 27 a = 27 3 = 9 High Level 5**

Let’s make this question into a low level 5 question. We know how to solve those! 3a = This is the only bit that is different. We can use inverse operations to get rid of it. This says “add 8” 3a = 27 What is the inverse operation? a = 27 3 Subtract Look! A low level 5 question! = 9

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Level 6 Objective: Be able to solve linear equations with an unknown both sides.

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**5a + 3 = 2a + 12 5a = 2a + 12 - 3 5a = 2a + 9 5a – 2a = 9 3a = 9 a = 9**

Low level 6 5a + 3 = 2a + 12 Let’s start by removing this. 5a = 2a 5a = 2a + 9 Doing this removes the add 3, but remember to subtract 3 from the other side too! 5a – 2a = 9 This says add 3 Now, let’s remove this. 3a = 9 To “get rid of” our 2a, we have to subtract 2a What is the inverse operation? a = 9 A 3 = 3 Subtract 3

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**5(a - 4) = 3(a + 2) 5a - 20 = 3a + 6 5a = 3a + 6 + 20 5a = 3a + 26**

Expanding Brackets Tutorial High Level 6 5(a - 4) = 3(a + 2) 5a - 20 = 3a + 6 5a = 3a First expand the brackets (Click the tutorial button above if you cannot remember how to do this) Now we have a low level 6 question which can be solved just as before. 5a = 3a + 26 5a – 3a = 26 2a = 26 a = 13

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Level 7 Objective: Be able to solve linear equations with an unknown on one side, including problems where the coefficients are fractional

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Level 7

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Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve.

Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve.

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