The difference between one-half a number and the number is 8 find the number

The number is  48

Step-by-step explanation:

First, let's call the number we are looking for n.

We can then write "two-thirds of the number" as 2/3n

We can also write "one-half of a number" as 1/2n

Finally, we are told 1/2n is the same as 2/3n −8 or: 1/2n = 23n −8  

We can now solve for n: 1/2n − 2/3n = 2/3n −8 − 2/3n 1/2n − 2/3n = −8We next need to get the fractions over common denominators, in this case, 6 by multiplying each fraction by the necessary for of 1: (3/3) 1/2n − (2/2) 2/3n = −8 3/6n − 4/6n = −8 − 1/6n = −8.  

We can finally solve for n by multiplying by -6 to isolate n −6 ⋅(−1/6)n = −8⋅ − 6  

1n = 48

n =48