SOLUTION: Given that 2x + 2 ≤ 33, find the largest value of x if: a. x is an integer b. x is a prime number c. x is an even number d. x is an odd number e. x is a perfect s

Question 1189296: Given that 2x + 2 ≤ 33, find the largest value of x if:
a. x is an integer
b. x is a prime number
c. x is an even number
d. x is an odd number
e. x is a perfect square
f. x is a perfect cube
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

Everything is so obvious . . . that I don't know what to explain.

It is like chew gum . . .

What is the reason posting such banality to the forum ?

It is of the 2 x 2 = 4 level reasoning . . .

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Let's solve the given inequality for x.

If x is a real number, then the highest it can go is 15.5

Now onto the questions your teacher asked:
If x is an integer, then the highest x can go is x = 15.
If x is prime, then the highest it can go is x = 13
If x is even, then the highest it can go is x = 14
If x is odd, then the highest it can go is x = 15
If x is a perfect square, then the highest it can go is x = 9
If x is a perfect cube, then the highest it can go is x = 8

Relevant sets needed:
integers = {..., -3, -2, -1, 0, 1, 2, 3, ...}
prime numbers = {2, 3, 5, 7, 11, 13, 17, 23, ...}
even numbers = {..., -4, -2, 0, 2, 4, ...}
odd numbers = {..., -3, -1, 1, 3, 5, ...}
perfect squares = {1, 4, 9, 16, 25, ...}
perfect cubes = {1, 8, 27, 64, 125, ...}

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