x = number
x/2 = one half the number
one half of the number increased by 6
x/2 + 6
one half of the number increased by 6 is less than 35
x/2 + 6 < 35
subtract 6 from both sides
x/2 + 6 < 35 - 6
x/2 < 29
multiply both sides by 2
2(x/2) < 29 * 2
x < 58