Final answer:
By substituting z=1, z=2, and z=3 into each expression, it is determined that the expressions 9z - 4 - 3z and 2(3z-2) are equivalent, producing the values 2, 8, and 14, respectively, for each z value.
Step-by-step explanation:
To find the value of each expression for different values of z, we substitute the given values of z into the expressions.
For z = 1:
Expression 1: 9(1) - 4 - 3(1) = 9 - 4 - 3 = 2
Expression 2: 2(3(1) - 2) = 2(3 - 2) = 2(1) = 2
Expression 3: 9(1) - 4(1) - 3 = 9 - 4 - 3 = 2
For z = 2:
Expression 1: 9(2) - 4 - 3(2) = 18 - 4 - 6 = 8
Expression 2: 2(3(2) - 2) = 2(6 - 2) = 2(4) = 8
Expression 3: 9(2) - 4(2) - 3 = 18 - 8 - 3 = 7
For z = 3:
Expression 1: 9(3) - 4 - 3(3) = 27 - 4 - 9 = 14
Expression 2: 2(3(3) - 2) = 2(9 - 2) = 2(7) = 14
Expression 3: 9(3) - 4(3) - 3 = 27 - 12 - 3 = 12
The expressions 1 and 2 are equivalent, as they result in the same value for each z value.