ninayeyen wrote:

If 5 z – 3 < 3 z + 4, which of the following cannot be a value of \(z^{3}\) ?

A) 0

B) 1

C) 8

D) 27

E) 6

(Note: All the answer choices are perfect cubes except E, so we think it’s a typo. Choice E should be 64 instead of 6.)

5z - 3 < 3z + 4

2z < 7

z < 3.5

z^3 < 3.5^3

Since 64 = 4^3, it can’t be the value of z^3.

Alternate Solution:

If z^3 = 0, then z = 0. If z^3 = 1, then z = 1. If z^3 = 8, then z = 2. If z^3 = 27, then z = 3. The values z = 0, 1, 2 and 3 all satisfy the given inequality; therefore the answer must be E.

Answer: E

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