It is often known that, when changing subject of formula , it required additional mental brain work.This branch of mathematics always give some students problems when solving changing subject of formula.Toady, this insurance is well covered and i will brake every down to your understanding.It is very simple to change the subject of a formula.
In other to do this, Think of the formula and equation.Solve the equation for the letter which is to become the subject.There are some idea you can apply to help you solve this kind of mathematics.I should belief that we have come across some topics on math,that means we must use those method in solving them.Also, remember what you must do when you come across some exercises. Some topics like:
Square root of a numbers
Simple equation
Factorization of numbers
Quadratic Equation
Standard Form
Area of a Shape etc.
If you can solve the above topics and always remember their rules, that means you will be able to handle our today's topic.
Now, i'll give you some examples, just pay attention..
Example 1
Make x the subject of the formula
a = b(1 - x)
Clear the brackets.
a = b -bx
Re - arrange to give term in x on one side of the equation.
bx = b - a
Divide both sides by b
bx b - a
----------- = ------------
b b
b - a
x = -------------
b
The above example is the working that combine two mathematics topic: Quadratic equation and Simple equation.
Example 2
Make y the subject of formula
b + x
a = -------------
b - x
Clear the fractions.Multiply both sides by ( b - x).
a(b - x ) = b + x
ab - ax = b + x
To solve this, you have to collect terms in x on one side of the equation also.
ab - b = ax + x
Take x outside a bracket.
ab - b = x( a + 1 )
Divide both sides by ( a + 1 ).
ab - b x( a + 1 )
------------ = ----------------
( a + 1 ) ( a + 1 )
ab - b
------------- = x
( a + 1 )
ab - b
x = --------------
( a + 1 )
b( a - 1)
x = ------------------
a + 1
The above can only be solved if you know how to factorize equation.
The general method is to treat the formula as an equation and the new subject as unknown of the equation.There are many different formula, and it is not possible to give general rules for changing their subject. However, do not forget the point given.
1.Begin by clearing fractions,brackets and root sign.
2.Rearrange the formula so that all the terms that contain the new subject are on on side of the equal sign and the rest on the other side.
3. If more than one term contains the subject, take it it outside a bracket.
4. Divide both side by the bracket,then simplify as far as possible.
Exercise
Make the letter x the subject of the following equations
1. ax + b = x
2. a( a - b ) = b(c- x)
x
3. -------- + b = c
a
4. x² = a²
Solution
1. ax + b = x
To solve this, make sure you collect terms in x on one side of the equation.
ax - x = b
Take x outside a bracket.
x ( a - 1 ) = b
Share/ divide both sides by ( a - 1 )
x ( a - 1 ) b
-------------- = -----------
b
x = ----------
a - 1
2. Solve this.x( a - b ) = b(c- x)
Clear the brackets.
ax - bx = bc - bx
ax - bx + bx = bc
x ( a - b + b) = bc
Divide both sides by ( a - b + b)
x ( a - b + b) bc
-------------------- = ----------------
bc
x = --------------
a
x
3. -------- + b = c
a
Multiply both side by a
x + b = ac
Subtract b fro both sides/
x = ac - b
4. x² = a²
x = a
That is how to solve this kind of mathematics,just apply the basic mathematics rules that all.If you have any question please feel free to put them in the comments box.
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