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
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

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.

$$5x=5$$

$$5x\div5=5\div5$$

$$x=1$$

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.

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

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

$$x=34$$