Final answer:
The algebraic expressions for the given verbal expressions are x + 16 >= 32, 13x < 36, x - 9 > 21, and x/4 <= 15.
Step-by-step explanation:
a) The algebraic expression for 'the sum for x and 16 is greater than or equal to 32' would be x + 16 >= 32. This represents that when we add x and 16, the result is greater than or equal to 32.
b) The algebraic expression for 'the product of 13 and x is less than 36' would be 13x < 36. This represents that when we multiply 13 and x, the result is less than 36.
c) The algebraic expression for 'the difference of x and 9 is greater than 21' would be x - 9 > 21. This represents that when we subtract 9 from x, the result is greater than 21.
d) The algebraic expression for 'the ratio of x and 4 is less than or equal to 15' would be x/4 <= 15. This represents that when we divide x by 4, the result is less than or equal to 15.