Answer:
-3/2
Explanation:
To solve for x in the equation -|x+1| + |x| = 1, we need to consider different cases based on the possible values of x. Recall that the absolute value of a number is always non-negative.
Case 1: x ≥ -1
If x is greater than or equal to -1, then |x+1| = x+1 and |x| = x. Substituting into the equation, we get:
-(x+1) + x = 1
Simplifying and solving for x, we get:
-1 = 1
This equation has no solution, so there are no values of x in this case that satisfy the original equation.
Case 2: x < -1
If x is less than -1, then |x+1| = -(x+1) and |x| = -x. Substituting into the equation, we get:
-(-(x+1)) - x = 1
Simplifying and solving for x, we get:
x = -3/2
Therefore, the only solution to the equation -|x+1| + |x| = 1 is x = -3/2.