Question

Math ai tutor grade 9

arlos is using a number line to add another integer to –4. He begins by showing –4 on the number line, as shown below. Carlos adds the other integer on the number line and says that the sum is negative.

A number line going from negative 5 to positive 5. The area between negative 4 to 0 is highlighted.


Which is true of the number Carlos added to –4?
The number must be a negative integer.
The number must be a positive integer.
The number could be 3 or any integer less than 3.
The number could be 4 or any integer greater than 4.

Answer 1

The integer that Carlos added to –4 to result in a negative sum must be a negative integer. This is because adding two negative integers always results in a negative sum. The correct statement is: The number must be a negative integer.

Step-by-step explanation:

When Carlos adds another integer to – 4 and the sum is negative, we can determine the nature of the integer he added by understanding the rules of addition for integers. For the sum of two integers to be negative:

• If two positive integers add, the answer is positive (e.g., 3 + 2 = 5).
• If two negative integers add, the answer is negative (e.g., -4 + (-2) = -6).
• If one integer is negative and the other positive, and the negative is larger in absolute value, the answer will be negative (e.g., -5 + 3 = -2).

Since the sum in Carlos's case is negative, the integer he added must also be negative. If it were a positive integer, the sum could be positive or less negative, depending on the sizes of the integers involved. Therefore, the correct statement is:

“The number must be a negative integer.”

This satisfies the condition that the sum of Carlos's number, -4, and the integer he added is negative.