Final answer:
The correct statements about the relationship between a real number x and its absolute value |x| are: a. x = |x| when x is positive or zero, and c. x < |x| when x is negative. Therefore, the relationship between x and |x| can be determined based on the sign of x.
Step-by-step explanation:
If x is a real number, the correct statement about its relationship to |x| (the absolute value of x) can be evaluated by considering the definition of absolute value. If x is positive or zero, x is equal to |x|. If x is negative, x is less than |x| because the absolute value of a negative number is its positive counterpart.
Therefore, the most accurate statement reflecting the relationship between a real number x and its absolute value |x| is either x is equal to |x| when x≥0 (positive or zero), or x is less than |x| when x<0 (negative). Hence, the relationship can be determined and the correct answer to the given options is:
a. x = |x| (when x is positive or zero)
c. x < |x| (when x is negative)