The sum of two numvers is 38 the larver number is 11 more than half thr smaller number

X= smaller number
1/2x+11= larger number

Add the two above

x + (1/2x+11)= 38
Add like terms
1 1/2x + 11= 38
Subtract 11 from both sides
1 1/2x= 27
Change fraction to improper fraction
3/2x= 27
Multiply both sides by reciprocal (inverse) of fraction
(2/3)(3/2x) =(27)(2/3)
They cancel each other on the left
x= (27*2)/3
x= 54/3
x= 18 smaller number

1/2x+11
= 1/2(18)+11
=(1*18)/2+11
=9+11
=20 larger number

Hope this helps :)