Answer: -2
Step-by-step explanation: The value of a that would make the equation have only one solution is -2.
First, let's consider the case where a is positive. If a = 2, for example, then the equation becomes |x| - 8 = 2, which can be simplified to |x| = 10. This equation has two solutions: x = 10 and x = -10. Therefore, if a is positive, the equation has two solutions, and it does not have only one solution.
Next, let's consider the case where a is negative. If a = -2, for example, then the equation becomes |x| - 8 = -2, which can be simplified to |x| = 6. This equation has two solutions: x = 6 and x = -6. Therefore, if a is negative, the equation also has two solutions, and it does not have only one solution.
Now, let's consider the case where a is equal to zero. If a = 0, then the equation becomes |x| - 8 = 0, which can be simplified to |x| = 8. This equation has only one solution: x = 8. Therefore, if a is equal to zero, the equation has only one solution.
Finally, let's consider the case where a is a negative number that is not equal to zero. If a = -3, for example, then the equation becomes |x| - 8 = -3, which can be simplified to |x| = 5. This equation has only one solution: x = 5. Therefore, if a is a negative number that is not equal to zero, the equation also has only one solution.