Question

Two opposite integer are 12 unit apart on a number line .what are the integers?​

Answer 1

The two opposite integers that are 12 units apart on a number line are -6 and +6, as they are equidistant from zero and the total distance between them is 12 units.

Step-by-step explanation:

If two opposite integers are 12 units apart on a number line, it means that the distance between them is 12. To find these integers, we divide the distance by 2 to find the distance from 0 to each number, since they are opposites. The distance from 0 to each number will be 6 units. Therefore, the two integers are -6 and +6.

To understand why, let's consider the number line. If you start at zero and move 6 units to the right, you reach +6. If you start at zero and go 6 units to the left (in the opposite direction), you reach -6. The distance between +6 and -6 is 12 units, fulfilling the condition of the question.

Answer 2

If two opposite integer are 12 units apart on a number line, then the integers are -6 and 6.

Step-by-step explanation:

Let's solve the problem with a step-by-step approach.

Since we're dealing with two opposite integers that are 12 units apart on a number line, we're essentially looking for two numbers, let's call them A and B, such that one is the negative of the other, and the difference between them is 12.

Let's denote the positive integer as A, which means the negative integer will be -A, because opposites on the number line have the same absolute value but different signs.

The distance between two integers on the number line is the absolute difference between them. So, we need to find A such that:

|A - (-A)| = 12

When we subtract a negative number, it is equivalent to adding its positive counterpart. So the equation simplifies to:

|A + A| = 12

Since `A` is an integer, the absolute value of A + A is simply 2A, because adding a number to itself will always give a non-negative result, and thus, the absolute value sign can be dropped. So, our equation becomes:

2A = 12

Now, to find A, we divide both sides of the equation by 2:

A = 12/2

A = 6

So the positive integer is 6, and the opposite integer, which is negative, would be -6.

To summarize, the two opposite integers that are 12 units apart on a number line are 6 and -6.