Half of a number added to its third part is eight less than the number. What is the number?

Let x to be the unknown
number.

In algebra, the verbal expression "half of
the number"  = x/2.

In the same way, the verbal expression
"the 3rd part" = x/3

We'll create the left side of the
equation:

Half of a number added to its third part is: x/2
+ x/3 =

In algebra, "is" means
"="

We'll create the right side of
equation:

"eight less than the number" x -
8

The equation is:

x/2 + x/3 =
x - 8

We'll multiply by 6 the
equation:

3x + 2x = 6x - 48

5x
- 6x = -48

-x = -48

x =
48

The unknown number is x =
48.