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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 

Rewrite 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 rewrite, so the largest number of x’s 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 Rewrite Divide by 8 

Multiply by 3x Rewrite 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. Rewrite 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
Rewrite 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 