Final answer:
The solution to the equation |x - 4| = x + 1 is x = 1.5
Step-by-step explanation:
The given equation is |x - 4| = x + 1.
To find the values of x that satisfy this equation, we can split it into two cases:
Case 1: (x - 4) = x + 1
Simplifying this case gives us -4 = 1, which is not true.
Therefore, there are no solutions in this case.
Case 2: (x - 4) = -(x + 1)
Simplifying this case gives us x - 4 = -x - 1.
Solving for x gives us x = 1.5
So, the solution to the equation |x - 4| = x + 1 is x = 1.5