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GCSE: Linear Equation Solving Part 1

We will be adding more basic notes for equation solving in the Key Stage 3 section.

This will provide those who need more detail on the fundamental ideas to really get to grips with the concepts.

We will add it as a link to the GCSE section when it is ready

For the moment, these provide a suitable set of exemplar examples and act as a check list for ideas which you may wish to grasp to access the higher grades at GCSE

 

 

Contents

1)           Basic equation

2)          Involving brackets

3)          Terms on both sides

4)          Fractions

 


 

Basic equation: Remember you use inverse functions

 

 

 

Add 2 to both sides

 

Divide by 5 (The coefficient)

 

 

 

Subtract 4 from each side

 

Divide by 7

 

 

 

Add 4 to both sides

 

Divide by 11.

This answer does not simplify

Leave as a fraction

 

 

 

Subtract 7 from both sides

 

Divide by 13

This answer does not simplify

Leave as a fraction

 

 

 

 

Re-write

 

Subtract 4 from both sides

 

Divide by 2

 

Involving brackets

Key: It will nearly always help to expand the bracket first.

 

 

 

 

Subtract 35 from both sides.

 

Divide by 5

 

This answer does not simplify

 

 

 

 

 

Add 35 to both sides

 

Divide by 10

 

Leave as a fraction

 

 

 

 

Ignore the +13 at first

 

Work out +8+13=+21

 

Subtract 21 from both sides

 

Divide both sides by 12

 


 

Terms on both sides: This will revise many of the concepts met in the first two sections.

The aim is to get it to look like one of the basic examples from section 1.

 

 

 

 

 

 

If we subtract 2x from both sides, look what happens. It becomes a simpler equation.

 

Now, take 3 from each side

 

Now divide by 2

 

 

 

 

Now we will add 4x to both sides

 

Add 7 to both sides

 

Divide by 15

 

 

 

 

Multiply out both brackets

 

 

Subtract 6x

 

Subtract 20

 

Divide by 4

 

 

 

 

Add x to each side

 

 

Add 1 to each side

 

Divide by 2

 

 

 

 

 

 

 

 

 

 

Expand the bracket first, ignore all the other terms for the moment

 

Simplify the 4x + 3x

 

For ease re-write, so the largest number of xs is on the left. (Makes it easier

 

Subtract 7x from each side

 

Subtract 9 from each side

 

Divide by 5

 


 

Equations with fractions: Part 1

 

 

Multiply both sides by 3

 

 

 

 

 

Multiply by 7

 

 

Divide by 2

 

 

 

 

Multiply by x

 

Re-write

 

Divide by 8

 

 

 

 

Multiply by 3x

 

Re-write

 

Divide by 30

 


 

Equations with fractions: Part 2

 

 

 

 

 

 

 

 

 

 

So this is the same as:

 

 

The denominators are 4,2 & 8

Find the Lowest Multiple (LCM) of these numbers. This is 8.

Re-write all the fractions with this as their denominator.

So:

 

 

If we now multiply by 8, the denominators all cancel.

 

Subtract 3

 

Divide by 2

 

This is the same as:

 

 

 

LCM of 7, 4 & 2 is 28

 

Multiply by 28

 

Add 7

 

Divide by 12

Equations with fractions: part 3

 

Re-write as:

 

 

 

 

So this is the same as

 

 

 

 

 

 

 

 

 

LCM of 5, 1 and 3 is 15

 

Multiply by 15

 

 

Expand

 

Simplify

 

Subtract 99

 

Divide by 3