# Chapter 10: Linear Equations

## Linear Equations

• To solve a linear equation you need to get the letter on its own on one side

• It is really important to write your working neatly when you are solving equations

• 5x + 3 = 18

• -3

• 5x = 15

• /5

• x=3

• Every line of working should have an equals sign in it

• Start a new line for each step, do one operation at a time

• Write down the operation you are carrying out, remember to do the same thing to both sides of the equation

• Line up the equals signs

## Letter on both sides

• To solve an equation you have to get the letter on its own on one side of the equations

• Start by collecting like terms so that all the letters are together

• 2 - 2x = 26 + 4x

• +2x

• 2 = 26 + 6x

• -26

• -24 = 6x

• /6

• -4 = x

## Equations with brackets

• Always start by multiplying out the brackets then collecting like terms

• 19 = 8 - 2(5 - 3y)

• 19 = 8 - 10 + 6y

• +2

• 21 = 6y

• 21/6 = y

## Examiners report

• Don’t use a trial and improvement method to solve an equation

• You probably won’t find the correct answer, and you can’t get any method marks

## Equations with fractions

• When you have an equation with fractions, you need to get rid of any fractions before solving

• You can do this by multiplying every term by the lowest common multiple of the denominators

• x/3 + x+1/5 = 11

• x15

• 5x + 3x-3 = 165

• +3

• 8x = 168

• /8

• x = 21

## Multiplying by an expression

• You might have to multiply by an expression to get rid of the fractions

• 20/n-3 = -5

• xn-3

• 20 = -5(n-3)

## Worked practice

• Eliminate fractions before you start solving the equation

• You can do this by multiplying both sides of the equation by 4

• Use brackets to show that you are multiplying everything by 4

• Multiply out the brackets, then solve the equation normally