If x is a nonzero real number,is x-2 always positive,always negative,or positive or negative depending on whether x is possible or negative explain
if x = 4, x-2 = 2
if x = 3, x-2 = 1
if x = 2, x-2 = 0
if x = 1, x-2 = -1
if x = 0, x-2 = -2
if x = -1, x-2 = -3
so + or - depending on if x greater than or less than 2
To determine whether x-2 is always positive, always negative, or positive or negative depending on whether x is positive or negative, we can apply some basic algebraic reasoning.
Let's consider the two scenarios:
1. x is positive:
If x is a positive real number, then subtracting 2 from a positive number will yield a positive result. This is because any positive number minus 2 is still greater than zero. Therefore, when x is positive, x-2 will always be positive.
2. x is negative:
If x is a negative real number, then subtracting 2 from a negative number will yield a negative result. This is because any negative number minus 2 is still less than zero. Therefore, when x is negative, x-2 will always be negative.
Hence, x-2 is positive when x is positive, and x-2 is negative when x is negative.
In summary, x-2 is positive or negative, depending on whether x is positive or negative, respectively. It is crucial to consider the sign of x to determine the sign of x-2.