Question - Solving Absolute Value Equation
Solution:
The given equation is |x - 1| = 8. To solve this equation for x, we need to consider both cases for the absolute value:Case 1: x - 1 is positive or zero. Then we have x - 1 = 8, which yields x = 8 + 1 = 9.Case 2: x - 1 is negative. Then we have -(x - 1) = 8, which simplifies to -x + 1 = 8 and then -x = 8 - 1 which gives us x = -7.So, the two possible values for x are 9 and -7. The question asks for "a possible value of x - 1". So we have to subtract 1 from each of our possible values for x:For x = 9, the value of x - 1 is 9 - 1 = 8.For x = -7, the value of x - 1 is -7 - 1 = -8.The value that matches one of the given answer choices is -8, which is option A.
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