Question: If x is an integer such that 3x + 5 is even, what can be said about x?
Options:
x is even
x is odd
x can be any integer
x is a prime number
Correct Answer: x is even
Solution:
For 3x + 5 to be even, x must be odd.
If x is an integer such that 3x + 5 is even, what can be said about x?
Practice Questions
Q1
If x is an integer such that 3x + 5 is even, what can be said about x?
x is even
x is odd
x can be any integer
x is a prime number
Questions & Step-by-Step Solutions
If x is an integer such that 3x + 5 is even, what can be said about x?
Correct Answer: x is odd
Step 1: Understand that an even number is any integer that can be divided by 2 without a remainder.
Step 2: Recognize that 3x + 5 is the expression we are analyzing.
Step 3: Note that 5 is an odd number.
Step 4: Remember that an odd number plus an even number results in an odd number, and an odd number plus an odd number results in an even number.
Step 5: Since we want 3x + 5 to be even, we need to determine what x must be.
Step 6: If x is even, then 3x (which is even) plus 5 (which is odd) would be odd. This does not satisfy our condition.
Step 7: If x is odd, then 3x (which is odd) plus 5 (which is odd) would be even. This satisfies our condition.
Step 8: Therefore, for 3x + 5 to be even, x must be odd.
Parity of Integers – Understanding how the sum of odd and even integers affects the overall parity (odd/even nature) of an expression.
Properties of Even and Odd Numbers – Knowing that an even number plus an odd number results in an odd number, while an even number plus an even number results in an even number.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
