i cannot figure out the number

Question

i have a number. add 8 to my number and the sum is less than twice my number.subtract 6 from my number and the difference is 1 less half my number. what is my number?

Answer 1

n=your number

n+8<2n

n-6=(n/2)-1

n-(n/2)-6=-1

n-(n/2)=6-1

(n/2)=5

n=10 is your number

check:10+8=18 and 18<2(10)

10-6=(1/2)(10)-1

4=5-1

4=4

 

Answer 2

a) x + 8 < 2x

 

b) x - 6 = x/2 - 1

 

From a, 8 < x.

 

 

From b, 2x - 12 = x - 2

 

x = 10

 

8 < 10.