Final answer:
The equation that represents the acceptable height range for NASA astronauts is d) |x - 68.5| = 6.5, which reflects the range of 62 to 75 inches.
Step-by-step explanation:
The question is asking for the equation that represents the acceptable height range for NASA astronauts. Absolute value equations are typically used to express a range of numbers. The absolute value of a difference like |x - a| expresses the distance of x from a, regardless if x is smaller or greater than a.
The correct equation must consider NASA's historic astronaut height requirements: astronauts are typically required to be between 62 and 75 inches tall. Therefore, the acceptable range is 13 inches (75 - 62) from the mid-point 68.5 inches (the average of 62 and 75).
Using the absolute value notation, we can represent this requirement as |x - 68.5| = 6.5, where x is the astronaut's height. This equation correctly indicates that the astronaut's height must be within 6.5 inches of 68.5 inches, which covers the range from 62 to 75 inches. Therefore, the answer is d) |x - 68.5| = 6.5.