1. The problem is to solve the equation $$|x - 1| = 5$$ where the expression inside the absolute value is $x - 1$. 2. Recall that the absolute value equation $|A| = B$ means $A = B$ or $A = -B$ when $B \geq 0$. 3. Applying this rule here, we set up two equations: $$x - 1 = 5$$ and $$x - 1 = -5$$ 4. Solve each equation separately: For $$x - 1 = 5$$: $$x = 5 + 1 = 6$$ For $$x - 1 = -5$$: $$x = -5 + 1 = -4$$ 5. Therefore, the solutions to the equation $$|x - 1| = 5$$ are $$x = 6$$ and $$x = -4$$. 6. These solutions satisfy the original absolute value equation because substituting back gives: $$|6 - 1| = |5| = 5$$ and $$|-4 - 1| = |-5| = 5$$ which confirms both are correct. Final answer: $$x = 6 \text{ or } x = -4$$