Algebra-1

The correct option is C. x = 1, x = -1.

To solve the equation | -x | = 1, we can consider two cases:

Case 1: -x is positive or zero (|-x| = x)
In this case, we can rewrite the equation as x = 1, which means x is equal to 1.

Case 2: -x is negative (|-x| = -(-x) = x)
In this case, we can rewrite the equation as -x = 1, which means x is equal to -1.

Combining both cases, we have x = 1 and x = -1, which means both values satisfy the equation.

Let's examine the other options to understand why they are not correct:

A. x = 1: This option suggests that x equals 1. As disc...