Question

If 1 < x, simplify the expression |1-x|.
a) x-1
b) 1-x
c) x+1
d) -x+1

Answer 1

Option A. When 1 < x, the simplified expression |1-x| is x-1. We need to consider the different cases based on the value of x.

Step-by-step explanation:

If 1 < x, we need to simplify the expression |1-x|. Since x is greater than 1, the expression (1-x) will be negative, so the absolute value will change the sign to make it positive. Therefore, the simplified form of |1-x| when 1 < x is x-1.

Let's consider an example. Suppose x is 2, then |1-2| = |-1|, which equals 1, and if we simplify it using our rule, it would be 2-1, which is also 1, confirming our simplification.

When simplifying the expression |1-x|, we need to consider the different cases based on the value of x.

1. If x is greater than 1, then |1-x| = 1-x.
2. If x is less than 1, then |1-x| = x-1.

Therefore, when 1 < x, the simplified expression |1-x| can be written as x-1 (option a).