Could someone please help me with this?
(1) If x is a nonzero real number, is x–2 always positive, always negative, or positive or negative depending on whether x is positive or negative? Explain your answer.
let x =10
then (x-2) = 8 which is positive
let x = -5
then x-2 = -7 which is negative,
so ......
what do you think?
To determine whether x–2 is always positive, always negative, or positive or negative depending on the value of x, we can break it down by considering different cases for x.
Case 1: x is positive.
If x is positive, then subtracting 2 from it (x–2) will still result in a positive value. For example, if x = 3, then 3–2 = 1, which is positive. Therefore, for positive values of x, x–2 is always positive.
Case 2: x is negative.
If x is negative, then subtracting 2 from it (x–2) will result in a smaller negative value. For example, if x = -3, then -3–2 = -5, which is negative. Therefore, for negative values of x, x–2 is always negative.
Case 3: x is zero.
If x = 0, then subtracting 2 from it (x–2) will give us -2, which is negative. Therefore, for x = 0, x–2 is negative.
Based on these cases, we can conclude that x–2 is positive when x is positive, x–2 is negative when x is negative, and x–2 is negative when x equals 0. Therefore, x–2 is positive or negative depending on whether x is positive or negative.