If x > y and y > z, which of the follow...
If x > y and y > z, which of the following represents the greatest number?
• a)
x-z
• b)
x-y
• c)
y-x
• d)
z-y
• e)
z-x
If x > y and y > z, which of the following represents the greate...
From x > y and y > z, it follows that x > z.
These inequalities imply the following about the differences that are given in the answer choices:
Since the expressions in A and B represent positive numbers and the expressions in C, D, and E represent negative numbers, the latter can be eliminated because every negative number is less than every positive number. To determine which of x - z and x - y is greater, consider die placement of points widi coordinates x, y, and x on the number line,

The distance between x and z (that is, x  - z) is the sum of the distance between x andy (that is, x - y) and the distance between y and z (that is, y - z).
Therefore (x- z) > (x y),which means that x-z represents the greater of the numbers represented by (x - z) and (x - y). Thus, x-z represents the greatest of the numbers represented by&e answer choices.
Alternatively,
y > z given
-y < -z multiply both sides by -1
x - y < x - z add x to both sides
Thus, x - z represents the greater of the numbers represented by (x - z) and (x - y). Therefore, x - z represents the greatest of the numbers represented by the answer choices.
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