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.

Brackets
I
ndices
D
ivision
M
ultiplication
A
ddition
S
ubtraction

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

Subtraction
Addition
M
ultiplication
D
ivision
Indices
B
rackets

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

Answer

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

Answer

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