Solve the equation. Check for extraneous solutions.
2|x - 7| = x - 8
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To solve this equation, we will remove the absolute value bars and check for extraneous solutions.
Case 1: x - 7 is positive
2(x - 7) = x - 8
2x - 14 = x - 8
x = 6
Checking: 2|6 - 7| = 6 - 8
2|(-1)| = -2
2 = -2 (Extraneous solution)
Case 2: x - 7 is negative
2(-x + 7) = x - 8
-2x + 14 = x - 8
-3x = -22
x = 22/3
Checking: 2|22/3 - 7| = 22/3 - 8
2|1/3| = -2/3
2/3 = -2/3 (Extraneous solution)
Therefore, the original equation has no valid solution.