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

Remember that your answer could be a fraction

# 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

Remember that your answer could be a fraction