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- I am an even integer between -3 and 7 - I am less than 6 but more than - 2
- I am not the additive inverse of - 6 - I am not equal to 4 + (-2)
- I am my own opposite THE MYSTIFY INTEGER is --------------------?

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Solution

The even integers between -3 and 7 are -2, 0, 2, 4 and 6Here 0 is an even integer because it can be written as an integral multiple of 2. That is, 0=2×0 for 0 belong to integers.Since the required integer is less than 6 and more than -2, it cannot be equal to either -2 and 6.Also, it is given that it is not an additive inverse of -6.The additive inverse of -6 is 6 because the sum of -6 and 6 equals 0, the additive identity.So now it is confimed that the number is not 6.Now we are left with only 3 integers 0, 2, 4It is further given that the number is not equal to 4+-2Evaluate 4+-2 as follows: 4+-2 =4-2 =2So the required number is not equal to 2.Now we are left with only two even integers 0 and 4.Apply the last condition that the required number is opposite of itself.Since the number 4 is not opposite of itself, we are left with only one even integer, 0The even integer 0 satisfies the condition that it is opposite of itself.Hence the required even integer is 0

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