**Solving Two Step Equations** *KS3 Revision*

## What you need to know

**Things to remember:**

- We do additions and subtractions first.
- We multiply or divide second.

We have previously heard the term **BIDMAS**, which tells us the order we do our operations in.

**B**rackets** I**ndices

**ivision**

D

D

**ultiplication**

M

M

**ddition**

A

A

**ubtraction**

S

S

We can use this to help us solve two step equations, but we look at it going backwards.

**S**ubtraction

**A**ddition** M**ultiplication

**ivision**

D

D

**I**ndices

**rackets**

B

B

*Solve the following linear equation 3x-3=12*

We will solve this in two steps by getting the x by itself.

**Step 1: **Is there an addition or a subtraction? If yes, do the opposite.

We are subtracting 3, but we need to do the opposite, which is adding 3.

3x-3=12

3x-3+3=12+3

3x=15

**Step 2: **Is there a multiplication or a division? If yes, do the opposite.

We are multiplying by 3, but we need to do the opposite, which is dividing by 3.

3x=15

3x\div3=15\div3

x=5

*Solve the following linear equation \dfrac{x}{6}+1=8*

**Step 1: **Is there an addition or a subtraction? If yes, do the opposite.

We are adding 1, but we need to do the opposite, which is subtracting 1.

\frac{x}{6}+1=8

\frac{x}{6}+1-1=8-1

\frac{x}{6}=7

**Step 2: **Is there a multiplication or a division? If yes, do the opposite.

*Hint: **Remember, a fraction is just another way of writing a division.*

We are dividing by 6, but we need to do the opposite, which is multiplying by 6.

\frac{x}{6}=7

\frac{x}{6}\times6=7\times6

x=46

## Example Questions

**Question 1:** *Solve the following linear equation 5x+2=7*

**Step 1: **Is there an addition or a subtraction? If yes, do the opposite.

We are adding 2, but we need to do the opposite, which is subtracting 2.

5x+2=7

5x+2-2=7-2

5x=5

**Step 2: **Is there a multiplication or a division? If yes, do the opposite.

We are multiplying by 5, but we need to do the opposite, which is dividing by 5.

5x=5

5x\div5=5\div5

x=1

**Question 2:** *Solve the following linear equation \dfrac{x}{2}-3=14*

**Step 1: **Is there an addition or a subtraction? If yes, do the opposite.

We are subtracting 3, but we need to do the opposite, which is adding 3.

\frac{x}{2}-3=14

\frac{x}{2}-3+3=14+3

\frac{x}{2}=17

**Step 2: **Is there a multiplication or a division? If yes, do the opposite.

*Hint: **Remember, a fraction is just another way of writing a division.*

We are dividing by 2, but we need to do the opposite, which is multiplying by 2.

\frac{x}{2}=17

\frac{x}{2}\times2=17\times2

x=34