How to make X the subject of a formula

Whatever you do to
one side, you do to the other

To make x the subject all you need to remember is whatever you do on one side you must do to the other

Let’s say…….An eye for an eye.

Example 1

Make P the subject of the formula $m=3n+2P$

Subtract 3n from BOTH SIDES

$m-3n=cancel(3n)+2P-cancel(3n)$

$m-3n=2P$

Divide both sides by 2

$(m-3n)/2=(cancel2P)/cancel2$

$(m-3n)/2=P$

$P=(m-3n)/2$

Now P is the subject to the formula.

Example 2

In the following formula:

$A=1/2(a+b)h$

Rearrange this formula to find the height h.

Multiply both sides by 2

$2A=cancel2times1/cancel2(a+b)h$

$2A=(a+b)h$

Divide both sides by (a + b)

$(2A)/(a+b)=(cancel((a+b))h)/cancel(a+b)$

$(2A)/((a+b))=h$

$h=(2A)/((a+b))$

Now the height h is the subject of the formula.

Example 3

The volume V of a cone is given by the formula:

$V=1/3pir^2h$

Rearrange this formula to find the radius r

Multiply both sides by 3

$3V=cancel3times1/cancel3pir^2h$

$3V=pir^2h$

Divide both sides by $pih$

$(3V)/(pih)=(cancelpir^2cancelh)/(cancel(pih)$

$(3V)/(pih)=r^2$

Take the square root of both sides

$sqrt(((3V)/(pih)))=cancelsqrt\(r^cancel2)$

$sqrt(((3V)/(pih)))=r$

$r=sqrt(((3V)/(pih)))$

Now the radius r is the subject of the formula