What is the value of 'a' when '4a-b=38' and 'b' has the value of '2'?

Firstly, we write down all the information we are given from the question into mathematical form.

This equation is 4a-b=38                                        The value of b is 2, so b=2                                          We are asked to find the value of a so a=?

1. To find out the value of 'a' we must first find out the value of 'b' and substitute it in the equation. The value of 'b' is already given to us as 2 . 

Substituting b=2  into 4a-b =38 gives us:

4a-(2)=38

We write the value of 'b' in brackets. If 'b' were '-2' then the equation would be 4a-(-2)=38 NOT 4a-2=38. 

2. We then open out the brackets in the equation so 4a-(2)=38 gives simply 4a-2=38 (since 2 is a positive number and a minus and positive sign next to each other gives a minus sign altogether).

If 'b' were '-2' and the brackets were then opened, 4a-(-2)=38 would give 4a+2=38, as a two minus signs next to each other give  a positive sign.

3. Once we have got out equation with the value of 'b' substituted in, we must rearrange the formula to find the value of 'a'.

4a-2=38

Whatever we do to one side of the equation, we must do to the other - since it is an equation. The aim is to have a by itself on the left hand side of the equation and its value on the right hand side, so we must undertake a series of mathematical steps (e.g. adding, subtracting, dividing or multiplying) to the left hand side of the equation to isolate a.

First, we must add 2 to the LHS of the equation, and then by rule the RHS too:

4a-2+2=38+2

This then leaves us with 4a=40

Then we must divide the LHS and RHS of the equation by 4.

4a/4=40/4

This gives us: a=10

We now have the answer to the question, as the value of 'a' is 10.

4. The next step is crucial, and it is to check your work by substituting your value of 'a' that you have just found and finding out the value of 'b'. If the value of 'b' that you obtain is 2, then your value of 'a' is correct.

The method for doing this is the same as above:

4a-b=38

a=10

i)   4(10)-b=38

ii)  (4x10)-b=38

iii)  40-b=38

iv) 40-40-b=38-40

v)   0-b=-2

vi)  -b=-2

vii)   b=2    (By multiplying both sides by '-1')

Successfully, b=2 when a=10 so your answer is correct and a has a value of 10 when 4a-b=38