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Try a vector approach.
If you're given the inequality and the equation, then the way to prove that they have the same solution is to solve each one and show that the solutions are the same number. Don't strain yourself, though. An inequality and an equation never have the same solution.
They are not. They are countably infinite. That is, there is a one-to-one mapping between the set of rational numbers and the set of counting numbers.
Arguments using numbers to prove their point.
Prime numbers and composite numbers are not used in daily jobs. However they are used by scientists to prove theorems.
If the imaginary part of z is 0, then z is simply a real number and if you multiply by 1 which is the identity in multiplication of real numbers, you of course will still have a real number with imaginary part 0
Find their GCF.
No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.
In this equation you would automatically add the numbers. The answer would be -12.
There is not much to prove there; opposite numbers, by which I take you mean "additive inverse", are defined so that their sum equals zero.
To prove that 61 is a prime number.
Yes. 0 is an integer and all integers are real numbers.