Expert: Josh - 11/15/2004

Question
(x-3)-1/3=1/5

Answer
Hello Pam,

The way the question reads, it contains no superscript whatsoever. So, the general idea is to separate (or isolate) the unknown quantity ("x") from the known ones -- using addition and subtraction.

Remember that whatever number you add, subtract, multiply or divide on one side of the equation, you must do the same to the other side AT ALL TIMES.

In this example, we can solve the equation following these steps.

(x-3)-1/3=1/5

Step 1: Add 1/3 on both sides of the equation.

(x-3)-1/3+(1/3)=(1/5)+(1/3)  ......[Line 1]
...obviously, the one third on the left hand side (LHS) of the equation cancels out, so we are left with
(x-3)=(1/5)+(1/3)   ......[Line 2]

Step 2: Adding the fractions (1/5)+(1/3).
Here, the common denominator is 5 x 3 =15.
Notice that we don't change anything if we multiply (1/5) bu (3/3). After all, 3/3 is one. Similarly, we don't change anything if we multiply (1/3) by (5/5).

Aim: we want to convert (1/5) to X/15 and (1/3) to Y/15, so that we can add them together directly and reduce it to a single fraction.

How to do this: Observe that
(1/3)=(1/3)x(5/5)
    =(1x5)/(3x5)
    =5/15   (i.e., X=5)
(1/5)=(1/5)x(3/3)
    =(1x3)/(5x3)
    =3/15   (i.e., Y=3)
So, (1/3)+(1/5)=(5/15)+(3/15)=8/15

Resuming from [Line 2] (see above), we have

(x-3)=8/15

Step 3: Adding 3 to both sides
x=3+(8/15).

This is equivalent to (3*15+8)/15 = 53/15 as an improper fraction.

Cheers.