Final answer:
To find the other solution to the equation |8-2x|-4=6, we set up two scenarios based on the absolute value. Solving these gives us x=-1 (known solution) and the other solution x=9.
Step-by-step explanation:
The equation |8-2x|-4=6 has two solutions, and we already know one solution is x=-1. To find the other solution, we need to consider that the absolute value equation |8-2x|=10 (after adding 4 to both sides) can lead to two scenarios:
8 - 2x = 10
8 - 2x = -10
From the first scenario, subtracting 8 from both sides gives us -2x = 2, and dividing by -2 gives us x = -1, which is the known solution. From the second scenario, subtracting 8 from both sides gives us -2x = -18, and dividing by -2 leads us to x = 9, which is the other solution to the equation.