Question

If z is a positive integer, does 4 + 3(2z-5) represent a number that is greater than,less than ,or equal to 2(3z-4)? Please show me how you got the answer.

Answer 1

4 + 3( 2(4) - 5)
= 4 + 24-5
= 28-5
= 23

2(3(4) -4)
= 2(12) -4
= 24 -4 = 20



4+3(2z-5) > 2(3z-4)

Answer 2

The number will be greater than 2(3z-4)

Explanation:

Thinking process:

Let the expressions be:

4 + 3(2z-5) ...1

and

2(3z-4) ...2

Now, let z be a positive number, say 2

Substituting gives:

4 + 3(2*2-5) = 7 ...1

and

2(3*2-4) = 4 ...2

As it can be seen from the solutions, the expression 4 + 3(2z-5) will be greater than 2(3z-4) for any value of z.

That is, 4 + 3(2z-5) > 2(3z-4) for any real value of z.