We will explain if the given radical equation is always, sometimes, or never true.
sqrt((x-2)^2)=x-2
Recall that when finding the principal square root of an expression including a variable, we have to be sure that the result is non-negative. Note that the given equation is not true for x<2 because if x is less than 2, then the result will be negative. As an example, let's substitute x= 1 in the equation and check if it produces a true statement.
As we can see, the equation is not true for 1. On the other side, it is true for x≥ 2 because if x is greater than or equal to 2, then the result will not be negative. To illustrate, let's substitute x= 3 into the equation and check if it makes the equation true.
