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 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   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