Final answer:
None of the inequalities provided (options b to d) inherently have no solutions. Option a is not an inequality. Options b and c have infinite solutions within their respective ranges, and option d has a single solution.
Step-by-step explanation:
To determine which of the following inequalities has no solutions, we must analyze each one:
- a. √x - 23: This expression is incomplete and not an inequality.
- b. √x < 23: The square root of any non-negative number x can be less than 23. There are infinite solutions for x as long as x is between 0 and 529 (since 23² = 529).
- c. √x > 23: The square root of any non-negative number x can be greater than 23. There are solutions for x as long as x is greater than 529.
- d. √x = 23: This is a simple equation with only one solution, which is x = 529, not an inequality.
Given this assessment, none of the options presented (a to d) technically describes an inequality with no solutions.