The distance between two numbers on the number line is 15. If one of the numbers is 5, what are the two possibilities for the other number?
It could be 20 or -10
i think the answer of the 2 numbers one is 15 and One is 5 it would be 10.
or 20
To find the two possibilities for the other number, we can use the concept of absolute value. The distance between two numbers on the number line is equal to the absolute value of their difference.
In this case, the given distance between the two numbers is 15. Let's denote the other number as x.
We know that the absolute value of the difference between 5 and x is 15. So, we can write the equation as:
|x - 5| = 15
To solve this equation, we need to consider two cases: when (x - 5) is positive and when it is negative.
Case 1: x - 5 is positive
If (x - 5) is positive, then we have:
x - 5 = 15
Adding 5 to both sides of the equation, we get:
x = 15 + 5
x = 20
So, one possibility for the other number is 20.
Case 2: x - 5 is negative
If (x - 5) is negative, then we have:
-(x - 5) = 15
Multiplying both sides of the equation by -1, we get:
x - 5 = -15
Adding 5 to both sides of the equation, we get:
x = -15 + 5
x = -10
So, the other possibility for the other number is -10.
Therefore, the two possibilities for the other number are 20 and -10.