Question

Which of the following represents the statement "z is less than d units from y"?

a) |z - y| < d
b) |z + y| < d
c) |z - y| > d
d) |z + y| > d

Answer 1

The correct representation is option (a) |z - y| < d.

Step-by-step explanation:

The correct representation of the statement 'z is less than d units from y' is option (a) |z - y| < d.

To understand this, let's break it down. The expression |z - y| represents the absolute value of the difference between z and y. When this absolute value is less than d, it means that the distance between z and y is less than d units.

For example, if z = 4 and y = 8, and d = 6, then |z - y| = |4 - 8| = |-4| = 4, which is less than d. Therefore, option (a) is the correct representation.